Trust Management in Online SocialNetworks
by
Guanfeng Liu
A thesis submitted in fulfillment
of the requirements for the degree of
Doctor of Philosophy
in the
Department of Computing
Faculty of Science
Macquarie University
Supervisor: A/Prof. Yan Wang
Associate Supervisor: Prof. Mehmet A. Orgun
2013
c© Copyright by
Guanfeng Liu
2013
Statement of Candidate
I certify that the work in this thesis entitled “Trust Management in Online Social
Networks” has not previously been submitted for a degree nor has it been submitted
as part of requirements for a degree to any other university or institution other than
Macquarie University.
I also certify that the thesis is an original piece of research and it has been written
by me. Any help and assistance that I have received in my research work and the
preparation of the thesis itself have been appropriately acknowledged.
In addition, I certify that all information sources and literature used are indicated
in the thesis.
Guanfeng Liu
17 June 2013
To my parents,
Zhenhua Liu and Yalin Sun,
who dedicated all their life to me
Abstract
Online Social Networks (OSNs) have attracted many participants, and they have been
used as a means for a rich variety of activities, such as movie recommendations and
product recommendations. In these activities, trust is one of the most important factors
for participants’ decision-making. Therefore, it is necessary and significant to evaluate
the trust between two participants who have no direct interaction. This thesis aims to
provide effective and efficient trust management methods to compute reasonable trust
evaluation results, which can be divided into the following three contributions.
The first contribution of the work is to study trust-oriented social network struc-
tures and solve the trust network extraction problem. To reflect the social networks in
the real world, we propose a complex trust-oriented social network structure, which
contains social contextual information that has significant influence on trust evalua-
tion. In addition, the trust network from a truster to a trustee without direct interac-
tions is extracted prior to performing trust evaluation. To extract a trust network that
can deliver trustworthy trust evaluation results, which is an NP-Complete problem, we
propose an approximation algorithm, called SCAN, and two new heuristic algorithms,
called SCAN-K and H-SCAN-K.
The second contribution of the work is to address the optimal social trust path
selection problem. To deal with the NP-Complete optimal social trust path selection
problem with multiple constraints, a novel approximation algorithm, called MONTE K,
and two novel heuristic algorithms, called H OSTP and MFPB-HOSTP, have been pro-
posed. In addition, we propose a heuristic algorithm, called H-OSTP-K, for K optimal
social trust paths selection.
The third contribution of the work is to study trust transitivity in OSNs. In order
to compute a reasonable propagated trust value along a social trust path, a general
v
vi
concept, called Quality of Trust Transitivity (QoTT) and a novel Multiple QoTT Con-
strained Trust Transitivity (MQCTT) model have been proposed.
For the proposed approaches, extensive experiments have been conducted on real
datasets or real scenarios. The experimental resulats have demonstrated the proposed
methods are superior to existing approaches in terms of the utility of delivered results
and efficiency.
Acknowledgments
First of all, I would like to express my sincere appreciation to my supervisor A/Prof.
Yan Wang and my associate supervisor Prof. Mehmet A. Orgun for their kindness
and patience. They have led me in the correct direction over the past few years not
only with their knowledge and experience, but also with thoughtfulness about a young
man’s personal growth. Literally, without their continuous support and endless guid-
ance, this work would not have been possible. It is my great fortune to have them as
my supervisors at Macquarie University.
I also would like to thank Prof. Ee-Peng Lim for his help in various stages of my
work. This academic journey would not have been so rewarding without his kindness
and wisdom.
In addition, my colleagues have helped me to develop this work. I wish to express
my thanks to Lei Li, Joe Zou and Haibing Zhang for providing a friendly and enjoyable
environment during these years.
Many thanks to the staff in the Department of Computing for their administrative
help. I would like to thank Sylvian Chow, Melina Chan, Donna Hua and Jackie Walsh
for their warm support and help.
Most important of all, I would like to thank my family. My parents, Zhenhua Liu
and Yalin Sun, have always been there for me. Their love, support and encouragement
have been the foundation for my life. I wish to thank them for all the opportunities
they have made available to me, and for the support they have given me during my
life. Thanks to my wife, Tong Tong, for her love, understanding and support. With-
out their love, unwavering support and inspiration, this work could never have been
accomplished.
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viii
Publications
[1] Guanfeng Liu, Yan Wang, Mehmet A. Orgun and Ee-Peng Lim, Finding the
Optimal Social Trust Path for the Selection of Trustworthy Service Providers
in Complex Social Networks, IEEE Transactions on Services Computing (TSC)
(regarded as the best journal in the field of services computing), Vol. 6, No. 2,
2013, pp. 152-167.
[2] Guanfeng Liu and Yan Wang, Trust-Oriented Service Provider Selection in
Complex Online Social Networks, A. Bouguettaya et.al (Ed.), Handbook on
Web Services, Springer, accepted on 03 Sep., 2012.
[3] Guanfeng Liu, Yan Wang and Mehmet A. Orgun, Social Context-Aware Trust
Network Discovery in Complex Contextual Social Networks, Twenty-Sixth AAAI
Conference on Artificial Intelligence (AAAI-12) (ERA rank A conference1),
22-26 August, 2012, Toronto, Canada, pp. 101-107.
[4] Guanfeng Liu, Yan Wang, Mehmet A. Orgun and Huan Liu, Discovering Trust
Networks for the Selection of Trustworthy Service Providers in Complex Con-
textual Social Networks, IEEE The 9th International Conference on Web Ser-
vices (IEEE ICWS 2012) (ERA rank A conference), 24-29 June, 2012, Hon-
olulu, Hawii, USA, pp. 384-391.
[5] Guanfeng Liu, Yan Wang and Duncan S. Wong, Multiple QoT Constrained
Social Trust Path Selection in Complex Social Networks, The 11th IEEE In-
ternational Conference on Trust, Security and Privacy in Computing and Com-
munications (TrustCom-2012) (ERA rank A conference), 25-27 June, 2012,
Liverpool, UK, pp. 624-631.
1refer to http://core.edu.au/index.php/categories/conference rankings
ix
x Publications
[6] Guanfeng Liu, Yan Wang and Mehmet A. Orgun, Trust Transitivity in Com-
plex Social Networks, Twenty-Fifth AAAI Conference on Artificial Intelligence
(AAAI-11) (ERA rank A conference), 7-11 August, 2011, San Francisco, Cal-
ifornia, USA, pp. 1222-1229.
[7] Guanfeng Liu, Yan Wang and Mehmet A. Orgun, Finding K Optimal Social
Trust Paths for the Selection of Trustworthy Service Providers in Complex So-
cial Networks, The 9th International Conference on Web Services (IEEE ICWS
2011) (ERA rank A conference), 4-9 July, 2011, Washington DC, USA, pp.
41-48.
[8] Guanfeng Liu, Yan Wang and Mehmet A. Orgun, Optimal Social Trust Path
Selection in Complex Social Networks, The Twenty-Fourth AAAI Conference
on Artificial Intelligence (AAAI 2010) (ERA rank A conference), 11-15 July,
2010, Atlanta, Georgia, USA, pp. 1391-1398.
[9] Guanfeng Liu, Yan Wang and Mehmet A. Orgun, Quality of Trust for Social
Trust Path Selection in Complex Social Networks, The 9th International Con-
ference on Autonomous Agents and Multiagent Systems (AAMAS2010) (ERA
rank A conference), 10-14, May 2010, Toronto, Canada, pp. 1575-1576.
[10] Guanfeng Liu, Yan Wang, Mehmet A. Orgun and Ee-Peng Lim, A Heuristic Al-
gorithm for Trust-Oriented Service Provider Selection in Complex Social Net-
works, IEEE The 7th International Conference on Services Computing (IEEE
SCC2010) (ERA rank A conference, the Best Paper Award), 5-10, July 2010,
Miami, Florida, USA, pp. 130-137.
[11] Guanfeng Liu, Yan Wang and Mehmet A. Orgun, Trust Inference in Complex
Trust-oriented Social Networks, 2009 International Conference on Computa-
tional Science and Engineering, 29-31, August, 2009, Vancouver, Canada, pp.
996-1001.
xi
[12] Guanfeng Liu, Yan Wang and Lei Li, Trust Management in Three Generations
of Web-Based Social Networks, International Workshop on Cyber Physical and
Social Computing (CPSC09), in conjunction with ATC-09, 7-9 July, 2009, Bris-
bane, Australia, pp. 446-451.
xii
Contents
Abstract v
Acknowledgments vii
Publications ix
1 Introduction 1
1.1 Challenges in the Trust Management of OSNs . . . . . . . . . . . . . 3
1.1.1 Trust Network Extraction . . . . . . . . . . . . . . . . . . . . 3
1.1.2 Social Trust Path Selection . . . . . . . . . . . . . . . . . . . 5
1.1.3 Trust Transitivity . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2 Contributions of the Work . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Roadmap of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Literature Review 11
2.1 Online Social Networks (OSNs) . . . . . . . . . . . . . . . . . . . . 11
2.1.1 Social Network Properties . . . . . . . . . . . . . . . . . . . 12
2.1.2 The New Categorisation of OSNs . . . . . . . . . . . . . . . 13
2.2 What is Trust? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.1 Definitions of Trust . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.2 Properties of Trust . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.3 The Influence of Trust on Human Activities . . . . . . . . . . 22
2.3 Trust Related Issues in OSNs . . . . . . . . . . . . . . . . . . . . . . 23
2.3.1 Trust Evaluation in OSNs . . . . . . . . . . . . . . . . . . . 23
2.3.2 Trust Network Extraction in OSNs . . . . . . . . . . . . . . . 25
2.3.3 Trust Path Selection in OSNs . . . . . . . . . . . . . . . . . . 28
xiii
xiv Contents
2.3.4 Trust Transitivity in OSNs . . . . . . . . . . . . . . . . . . . 29
2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3 Contextual Trust-Oriented Social Networks 33
3.1 Social Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1.1 Independent Social Environments . . . . . . . . . . . . . . . 34
3.1.2 Dependent Social Environments . . . . . . . . . . . . . . . . 35
3.2 Social Contextual Impact Factors . . . . . . . . . . . . . . . . . . . . 36
3.2.1 Trust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2.2 Social Intimacy Degree . . . . . . . . . . . . . . . . . . . . . 36
3.2.3 Community Impact Factor . . . . . . . . . . . . . . . . . . . 37
3.2.4 Preference Similarity . . . . . . . . . . . . . . . . . . . . . . 38
3.2.5 Residential Location Distance . . . . . . . . . . . . . . . . . 38
3.3 A Contextual Trust-Oriented Social Network Structure . . . . . . . . 39
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4 Trust Network Extraction in Large-Scale Trust-Oriented Social Networks 41
4.1 The Trust Network Extraction Problem . . . . . . . . . . . . . . . . . 41
4.2 Social Context-Aware Trust Network Extraction Models . . . . . . . 44
4.2.1 The Influence of Social Context on Social Interactions and So-
cial Connections . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2.2 Quality of Trust Network (QoTN) . . . . . . . . . . . . . . . 46
4.2.3 Trust Network Utility . . . . . . . . . . . . . . . . . . . . . . 47
4.3 The Proposed SCAN Algorithm for Trust Network Extraction . . . . 47
4.3.1 Monte Carlo Method . . . . . . . . . . . . . . . . . . . . . . 49
4.3.2 Algorithm Description of SCAN . . . . . . . . . . . . . . . . 49
4.3.3 The Process of SCAN . . . . . . . . . . . . . . . . . . . . . 51
4.4 Experiments on SCAN . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.4.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . 54
4.4.2 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . 55
Contents xv
4.5 The Proposed H-SCAN for Trust Network Extraction . . . . . . . . . 57
4.5.1 K-Best-First Search (KBFS) . . . . . . . . . . . . . . . . . . 57
4.5.2 Algorithm Description of H-SCAN . . . . . . . . . . . . . . 58
4.5.3 The Process of H-SCAN . . . . . . . . . . . . . . . . . . . . 59
4.6 The Proposed H-SCAN-K for Trust Network Extraction . . . . . . . 62
4.6.1 Drawbacks of H-SCAN . . . . . . . . . . . . . . . . . . . . 62
4.6.2 Algorithm Description of H-SCAN-K . . . . . . . . . . . . . 63
4.6.3 The Process of H-SCAN-K . . . . . . . . . . . . . . . . . . . 67
4.7 Experiments on H-SCAN and H-SCAN-K . . . . . . . . . . . . . . . 71
4.7.1 Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.7.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . 72
4.7.3 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . 73
4.7.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5 Finding the Optimal Social Trust Path 83
5.1 Quality of Trust (QoT) and QoT Attributes Aggregation . . . . . . . . 84
5.1.1 Quality of Trust (QoT) . . . . . . . . . . . . . . . . . . . . . 84
5.1.2 QoT Attribute Aggregation . . . . . . . . . . . . . . . . . . . 85
5.1.3 Utility Function . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.2 The Proposed MONTE K for Optimal Social Trust Path Selection . . 87
5.2.1 Existing Approximation Algorithms . . . . . . . . . . . . . . 88
5.2.2 Algorithm Description of MONTE K . . . . . . . . . . . . . 89
5.2.3 The Process of MONTE K . . . . . . . . . . . . . . . . . . . 90
5.3 Experiments on MONTE K . . . . . . . . . . . . . . . . . . . . . . . 93
5.3.1 Experiment Settings . . . . . . . . . . . . . . . . . . . . . . 93
5.3.2 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . 94
5.4 The Proposed H OSTP for Optimal Social Trust Path Selection . . . . 98
5.4.1 Algorithm Description of H OSTP . . . . . . . . . . . . . . . 99
xvi Contents
5.4.2 The Process of H OSTP . . . . . . . . . . . . . . . . . . . . 102
5.5 Experiments on H OSTP . . . . . . . . . . . . . . . . . . . . . . . . 104
5.5.1 Experiment Settings . . . . . . . . . . . . . . . . . . . . . . 104
5.5.2 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . 105
5.6 The Proposed MFPB-HOSTP for Optimal Social Trust Path Selection 108
5.6.1 The Advantage and Disadvantage of H OSTP . . . . . . . . . 108
5.6.2 Algorithm Description of MFPB-HOSTP . . . . . . . . . . . 111
5.6.3 The Process of MFPB-HOSTP . . . . . . . . . . . . . . . . . 113
5.6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.7 Experiments on MFPB-HOSTP . . . . . . . . . . . . . . . . . . . . 125
5.7.1 Experiment Settings . . . . . . . . . . . . . . . . . . . . . . 125
5.7.2 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . 127
5.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6 Finding K Optimal Social Trust Paths 135
6.1 K Optimal Social Trust Paths Selection . . . . . . . . . . . . . . . . 136
6.2 Existing Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
6.2.1 Category 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
6.2.2 Category 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.3 The Proposed H-OSTP-K for K Optimal Social Trust Paths Selection 138
6.3.1 Algorithm Description of H-OSTP-K . . . . . . . . . . . . . 138
6.4 Experiments on H-OSTP-K . . . . . . . . . . . . . . . . . . . . . . . 143
6.4.1 Experiment Settings . . . . . . . . . . . . . . . . . . . . . . 143
6.4.2 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . 144
6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
7 Trust Transitivity in Complex Contextual Trust-Oriented Social Networks153
7.1 Trust Properties and the Quality of Trust Transitivity . . . . . . . . . 154
7.1.1 The properties of Trust Transitivity . . . . . . . . . . . . . . 154
7.1.2 Quality of Trust Transitivity (QoTT) . . . . . . . . . . . . . . 156
Contents xvii
7.1.3 QoTT Constraints . . . . . . . . . . . . . . . . . . . . . . . 156
7.2 Multiple QoTT Constrained Trust Transitivity Model . . . . . . . . . 157
7.2.1 The Process of MQCTT . . . . . . . . . . . . . . . . . . . . 157
7.3 Experiments on MQCTT . . . . . . . . . . . . . . . . . . . . . . . . 162
7.3.1 Experiment Settings . . . . . . . . . . . . . . . . . . . . . . 162
7.3.2 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . 163
7.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
8 Conclusions and Future Work 169
8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
8.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
9 Notations Used in This Thesis 173
Bibliography 179
xviii Contents
List of Figures
1.1 A trust-oriented social network . . . . . . . . . . . . . . . . . . . . . 3
3.1 A contextual trust-oriented social network . . . . . . . . . . . . . . . 39
4.1 A sub trust network (TN-part-1) . . . . . . . . . . . . . . . . . . . . 42
4.2 A sub trust network (TN-part-2) . . . . . . . . . . . . . . . . . . . . 42
4.3 The influence of social context on social connections . . . . . . . . . 45
4.4 Normal distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.5 Unsatisfied nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.6 The utilities of extracted trust networks with 4 hops . . . . . . . . . . 53
4.7 The utilities of extracted trust networks with 6 hops . . . . . . . . . . 53
4.8 The execution time (4 hops) . . . . . . . . . . . . . . . . . . . . . . 54
4.9 The execution time (6 hops) . . . . . . . . . . . . . . . . . . . . . . 54
4.10 A case of accessing the node with deg+ = 0 . . . . . . . . . . . . . . 59
4.11 Repeated selecting the same expansion node in different search steps . 59
4.12 Drawbacks in H-SCAN . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.13 v−mg nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.14 v+mg nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.15 The property of bidirectional search . . . . . . . . . . . . . . . . . . 67
4.16 The average performance ratio delivered by TTL-BFS on Enron email
dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.17 The average performance ratio delivered by TTL-BFS on Epinions
dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.18 The comparison of average performance ratio on Enron email dataset 76
4.19 The comparison of average performance ratio on Epinions dataset . . 76
xix
xx LIST OF FIGURES
4.20 The average utilities delivered by H-SCAN-K+HS1 and H-SCAN-
K+HS2 on Enron email dataset . . . . . . . . . . . . . . . . . . . . . 77
4.21 The average utilities delivered by H-SCAN-K+HS1 and H-SCAN-
K+HS2 on Epinions dataset . . . . . . . . . . . . . . . . . . . . . . . 78
4.22 The average execution time of H-SCAN-K+HS1 and H-SCAN-K+HS2
on Enron email dataset . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.23 The average execution time of H-SCAN-K+HS1 and H-SCAN-K+HS2
on Epinions dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.1 Maximal length of paths is 4 hops . . . . . . . . . . . . . . . . . . . 94
5.2 Maximal length of paths is 5 hops . . . . . . . . . . . . . . . . . . . 95
5.3 Maximal length of paths is 6 hops . . . . . . . . . . . . . . . . . . . 95
5.4 Maximal length of paths is 7 hops . . . . . . . . . . . . . . . . . . . 96
5.5 The comparison in path utilities of sub-networks . . . . . . . . . . . . 105
5.6 The comparison in Execution time . . . . . . . . . . . . . . . . . . . 107
5.7 Limitation of H OSTP . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.8 Multiple CBLPs in backward search procedure . . . . . . . . . . . . 115
5.9 The CBLP in path selection . . . . . . . . . . . . . . . . . . . . . . . 115
5.10 The path utilities of sub-networks with 4 and 5 hops based on WID=1 127
5.11 The path utilities of sub-networks with 4 and 5 hops based on WID=2 128
5.12 The path utilities of sub-networks with 4 and 5 hops based on WID=3 128
5.13 The path utilities of sub-networks with 6 and 7 hops based on WID=1 129
5.14 The path utilities of sub-networks with 6 and 7 hops based on WID=2 130
5.15 The path utilities of sub-networks with 6 and 7 hops based on WID=3 130
5.16 The execution time of sub-networks with 4 and 5 hops . . . . . . . . 132
5.17 The execution time of sub-networks with 6 and 7 hops . . . . . . . . 133
6.1 The path utilities of sub-networks with each group of hops . . . . . . 145
6.2 The sum of path utilities with different K values . . . . . . . . . . . . 146
6.3 The execution time of K = 2 . . . . . . . . . . . . . . . . . . . . . . 147
LIST OF FIGURES xxi
6.4 The execution time of K = 3 . . . . . . . . . . . . . . . . . . . . . . 148
6.5 The execution time of K = 4 . . . . . . . . . . . . . . . . . . . . . . 150
6.6 The execution time of K = 5 . . . . . . . . . . . . . . . . . . . . . . 151
7.1 General trust decay with the increase of transitivity hops . . . . . . . 156
7.2 Trust transitivity model . . . . . . . . . . . . . . . . . . . . . . . . . 158
7.3 Increase of intersection angle θ . . . . . . . . . . . . . . . . . . . . . 161
7.4 Trust values computed based on different subjective impact parameters 164
7.5 The results of TSI − T ′SI . . . . . . . . . . . . . . . . . . . . . . . . 165
7.6 The results of TCIF − T ′CIF . . . . . . . . . . . . . . . . . . . . . . . 166
7.7 The results of TPS − T ′PS . . . . . . . . . . . . . . . . . . . . . . . . 167
xxii LIST OF FIGURES
List of Tables
1.1 Top 10 popular OSNs . . . . . . . . . . . . . . . . . . . . . . . . . . 2
4.1 The settings of QoTN constraints . . . . . . . . . . . . . . . . . . . . 55
4.2 The comparison of the utility . . . . . . . . . . . . . . . . . . . . . . 56
4.3 The comparison of execution time (5000 simulations) . . . . . . . . . 56
4.4 The settings of QoTN constraints . . . . . . . . . . . . . . . . . . . 72
4.5 Algorithms compared in the experiments . . . . . . . . . . . . . . . 72
4.6 Comparison of performance ratio . . . . . . . . . . . . . . . . . . . . 81
5.1 Properties of different social networks . . . . . . . . . . . . . . . . . 97
5.2 The properties of the simplest and the most complex sub-networks in
each group of hops . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.3 The comparison of utility . . . . . . . . . . . . . . . . . . . . . . . . 106
5.4 The comparison of execution time . . . . . . . . . . . . . . . . . . . 106
5.5 Social trust paths and the aggregated QoT attributes values . . . . . . 110
5.6 BLPs, CBLPs, and the aggregated QoT attributes values . . . . . . . 116
5.7 The setting of QoT constraints . . . . . . . . . . . . . . . . . . . . . 125
5.8 The setting of the weight of QoT attributes . . . . . . . . . . . . . . . 126
5.9 The properties of the simplest and the most complex sub-networks in
each group of hops . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
5.10 The comparison of path utility . . . . . . . . . . . . . . . . . . . . . 131
5.11 The comparison of execution time . . . . . . . . . . . . . . . . . . . 132
6.1 The setting of QoT constraints . . . . . . . . . . . . . . . . . . . . . 144
6.2 The comparison of path utility . . . . . . . . . . . . . . . . . . . . . 149
6.3 The comparison of execution time . . . . . . . . . . . . . . . . . . . 152
xxiii
xxiv LIST OF TABLES
7.1 Extracted sub-networks . . . . . . . . . . . . . . . . . . . . . . . . . 162
7.2 Selected trust transitivity models . . . . . . . . . . . . . . . . . . . . 162
7.3 Subjective impact parameters of three domains . . . . . . . . . . . . 163
9.1 Notations Used in Chapter 3 . . . . . . . . . . . . . . . . . . . . . . 173
9.2 Notations Used in Chapter 4 . . . . . . . . . . . . . . . . . . . . . . 174
9.3 Notations Used in Chapter 4 (continued) . . . . . . . . . . . . . . . . 175
9.4 Notations Used in Chapter 5 . . . . . . . . . . . . . . . . . . . . . . 175
9.5 Notations Used in Chapter 5 (continued) . . . . . . . . . . . . . . . . 176
9.6 Notations Used in Chapter 6 . . . . . . . . . . . . . . . . . . . . . . 176
9.7 Notations Used in Chapter 7 . . . . . . . . . . . . . . . . . . . . . . 177
Chapter 1
Introduction
The concept of social networks emerged in late 1800s. Ferdinand [35] and Emile [36]
proposed the idea of social networks in their theories and research of social groups in
1887 and 1893 respectively. Major developments in the research of social networks
occurred in the 1930s by research scientists in the disciplines of Psychology, Anthro-
pology, and Mathematics [118, 119]. For example, in the discipline of Psychology,
Moreno [119] systematically recorded and analysed the social interactions between
people in small groups, especially classrooms and work groups. In addition, in the
discipline of Sociology, Parsons [108] studied the social structure by analysing the so-
cial relationships between people. Furthermore, based on Parsons’ theory, the work
of sociologist Blau [13] provides a strong impetus for analysing the relational ties of
social units with his work on social exchange theory.
With the development of Internet and Web technology, Online Social Networks
(OSNs), such as Facebook (facebook.com) and Twitter (twitter.com), have attracted
many participants. According to statistics provided by The eBusiness Knowledgebase
(www.ebizmba.com, a Web statistic company) on 05 December 2012, the top 10 popu-
lar OSNs and the approximate number of the monthly unique visitors to them are listed
in Table 1.1. From the table, we can see that, for the most popular OSN, Facebook,
there are approximately 750,000,000 unique visitors visiting the Website in a month.
In recent years, social networking sites have been used as a means for a variety of activ-
ities. For example, according to a survey of 2600 hiring managers in 2009 by Career-
Builder (careerbuilder.com, a popular job hunting website), 45% of those managers
1
2 Introduction
used social networking sites to investigate potential employees. The ratio increased to
72% in January 2010. In addition, at FilmTrust (trust.mindswap.org/FilmTrust/), an
OSN for movie recommendations, participants can rate movies and make movie rec-
ommendations. Furthermore, by connecting with OSNs (e.g., Facebook and Twitter)
at some e-commerce websites like ThisNext (thisnext.com) and eBay (ebay.com), a
buyer can recommend the products available on these e-commerce websites to his/her
friends who participate in the OSNs. In these activities, trust is one of the most im-
portant factors for participants’ decision making. However, most of participants do
not have previous direct interactions, and thus require approaches and mechanisms for
evaluating the trustworthiness between participants who are unknown to each other.
Table 1.1: Top 10 popular OSNsRanking Name URL Unique Monthly Visitors
#1 Facebook facebook.com 750,000,000#2 Twitter twitter.com 250,000,000#3 Linkedin linkedin.com 110,000,000#4 Myspace myspace.com 70,500,000#5 Google Plus+ plus.google.com 65,000,000#6 DeviantArt deviantart.com 25,500,000#7 LiveJournal livejournal.com 20,500,000#8 Tagged tagged.com 19,500,000#9 Orkut orkut.com 17,500,000#10 Pinterest pinterest.com 15,500,000
An Online Social Network (OSN) can be represented as a graph, where each node
represents a participant and each link between two nodes corresponds to a real-world
or online interaction (e.g., A → B and B → C in Fig. 1.1). For adjacent participants
(i.e., those nodes with a directed link between them), the trust value between them
could be explicitly given by one to another based on their direct interaction (e.g., at
FilmTrust, a participant can recommend movies to his/her friends, and the correspond-
ing recommendee can give a trust rating (i.e., 1 to 10) to the recommender based on the
quality of the movie recommendation(s)). In OSNs, as each participant usually inter-
acts with many others, multiple trust paths may exist between nonadjacent participants
§1.1 Challenges in the Trust Management of OSNs 3
A B
D
E targetsource
C
TAB
TBC TCE
TBE
TBD TDE
Figure 1.1: A trust-oriented social network
from the source participant (e.g., A) to the target participant (e.g., E) (For example,
path A → B → C → E and A → B → D → E in Fig. 1.1). If there exists at least
one social trust path linking two unknown participants (e.g., A and E are linked by
three social trust paths), there exists a social connection between them. All such social
trust paths form a trust network from a source to a target (e.g., the trust network from
A to E in Fig. 1.1).
This thesis will focus on the three significant challenging problems of trust network
extraction, trust path selection and trust transitivity in the trust management of OSNs.
1.1 Challenges in the Trust Management of OSNs
1.1.1 Trust Network Extraction
In the social network depicted in Fig. 1.1, suppose A is looking for a badminton coach
and E is a badminton coach. In such a situation, as indicated in the theory of Social
Psychology [23, 91] and Computer Science [48, 78], A can evaluate the trustworthi-
ness of E based on the trust network from A to E by using trust transitivity methods
(e.g., A trusts B, and B trusts C, then A can trusts C to some extent. This is also
true in a long path from a source to a target) [48, 62]. Therefore, in OSNs, such a
trust network is fundamental and critical for trust evaluation between two nonadjacent
participants, as it contains some important intermediate participants, the trust relations
4 Introduction
between those participants and the social context. All of them have important influ-
ences on the trust evaluation between two unknown participants in OSNs.
In the literature, there have been several existing trust evaluation approaches for
trust evaluation between two nonadjacent participants [48, 83, 85]. However, they
all assume that the trust network between the two nonadjacent participants has been
identified. Therefore, given any two participants who have no direct interactions in
a large-scale social network, extracting the trust network between them becomes a
fundamental and essential step before performing any trust propagation methods. Such
a task is called trust network extraction.
In the graph formed by social interactions, cycles (e.g., path A → B → C →A) usually exist due to the complex interactions among multiple participants [103].
Extracting a sub network from a cyclic network has been proved to be an NP-Complete
problem [6]. Therefore, it is computationally infeasible to extract all the social trust
paths from a source and a target in a large-scale trust network. So, it is a significant
challenge to extract a trust network with higher quality that contains more important
intermediate nodes and social contexts and using such a trust network, one can deliver
more reasonable trust evaluation results with high efficiency.
In the literature, some resource discovery methods, developed for peer-to-peer
(P2P) networks, can be used for trust network extraction in OSNs. Those methods
include the Time To Live Breadth First Search (TTL-BFS) method [19, 37], the Ran-
dom Walk Search (RWS) method [45, 46] and the High Degree Search (HDS) method
[2]. But these methods do not consider the social context in social networks, includ-
ing social relationships between participants (e.g., the one between an employer and
an employee), the social position (e.g., a professor in service computing research),
the preference (e.g., like to play badminton) and the residential location (e.g., living in
Sydney, Australia) of participants. As indicated in Social Psychology [16, 75, 135], all
the above social contextual information has significant influence on both social interac-
tions and trust evaluation, and they can be discovered by using data mining techniques
[96, 123]. In addition, a source may have different purposes and needs when evalu-
§1.1 Challenges in the Trust Management of OSNs 5
ating the trustworthiness of a target, e.g., looking for a potential employee or looking
for a movie recommendation. Thus, in order to obtain a more reasonable and trustwor-
thy trust evaluation result, a source participant may specify some constraints on social
contexts as his/her trust evaluation criteria in trust network extraction. However, this
feature has not been supported in any of the existing methods.
1.1.2 Social Trust Path Selection
In an extracted large-scale trust-oriented social network, there could be tens of thou-
sands of social trust paths between a source participant and the target one [70]. Eval-
uating the trustworthiness of the target participant based on all these social trust paths
can incur huge computational time. Alternatively, we can search an optimal path yield-
ing the most trustworthy trust propagation result from multiple paths. This is called the
optimal social trust path selection problem that is known to be a challenging research
problem in OSNs [78].
In the literature, Lin et al. [77] proposed an optimal social path selection method.
In their model, the shortest path between the source participant and the target one is
selected as the optimal one. This method neglects trust information between partici-
pants. In another work [53], the path with the maximal propagated trust value is se-
lected as the most trustworthy social trust path. However, this work does not consider
the social contextual information introduced in the above Section 1.1.1, which has sig-
nificant influence on trust propagation [3, 102]. In addition, a source participant may
have different social trust path selection criteria (e.g., with more focus on the recom-
mendation roles of participants in employment and/or with more focus on the social
relationships between participants in making friends) and should be able to set certain
constraints on social context in trust propagation. This can help the source participant
select the optimal social trust path that yields the most trustworthy trust propagation
result. However, such a capability is not supported by any existing method.
6 Introduction
1.1.3 Trust Transitivity
After extracting the trust network and selecting the trustworthy social trust paths from
the trust network, the computation of the value of trust for the target participant re-
quires an understanding of how trust is propagated along a social trust path, which is a
critical and challenging problem in OSNs [48, 51]. In the literature, several trust tran-
sitivity models have been proposed [48, 50, 51, 113, 124], but they have the following
drawbacks.
Firstly, similar to the trust evaluation and trust path selection methods discussed in
Sections 1.1.1 and 1.1.2, these existing trust transitivity models do not fully consider
those important social contextual information, i.e., social relationship, social position
and preference that have significant influence on trust transitivity [3, 76, 102]. Sec-
ondly, although different trust evaluation criteria can influence trust transitivity results,
the specification of such criteria is not supported by any existing method either. Fi-
nally, trust transitivity formalised in existing models does not follow the nature of trust
decay illustrated in social psychology, namely, trust decays slowly in a certain number
of early hops (specified by a source participant) from a source participant, and then
decays fast until the trust value approaches the minimum [44, 61].
1.2 Contributions of the Work
Extracting the trust network between a source and a target is the first step for the trust
management in OSNs, as it is fundamental to performing any trust path selection and
trust evaluation methods. Based on the solution of trust network extraction, to effec-
tively and efficiently evaluate the trust between two unknown participants, we need to
select those trustworthy social trust paths and perform trust transitivity computation to
deliver reasonable trust values.
In order to address the above significant and challenging problems in the trust
management of OSNs, this thesis makes three major contributions.
§1.2 Contributions of the Work 7
1. The first contribution of this thesis is trust network extraction in large-scale trust-
oriented social networks.
(a) A novel complex trust-oriented contextual social network structure is pro-
posed. This new structure contains complex social contextual information,
including social relationships, social positions, preferences, residential lo-
cations. It can reflect the social networks in the real world better because
the above mentioned important social contextual information in the human
society is modeled in the new structure.
(b) We propose a new general concept, called QoTN (Quality of Trust Net-
work) which illustrates the trustworthiness of an extracted trust network.
Then we propose a social context-aware trust network extraction method
with QoTN constraints.
(c) To address the NP-Complete trust network extraction problem, we propose
an approximation algorithm, called SCAN, by adopting the Monte Carlo
method [43] and several optimization strategies. In addition, we propose
two heuristic algorithms, called H-SCAN and H-SCAN-K based on the
K-Best-First Search (KBFS) method [34], bidirectional search (i.e., search
from both the source node and the target node simultaneously) [57] and
our proposed optimization and heuristic search strategies.
Experiments conducted on real social network datasets illustrate that on
average, our methods can extract trust networks with higher quality and
consumes less execution time than the existing methods.
2. The second contribution of this thesis is social trust path selection.
(a) In service invocations, users can set multiple end-to-end constraints for the
attributes of QoS to satisfy their requirements (e.g., cost, delay and avail-
ability) of services. Different requirements have different constraints (e.g.,
8 Introduction
total cost<$20, delay<5s and availability>70%). Similar to QoS, we pro-
pose a novel concept Quality of Trust (QoT) that illustrates the trustworthi-
ness of the identified social trust paths. In our model, source participants
can also specify end-to-end QoT constraints to reflect their trust path selec-
tion criteria. Then the multiple QoT constrained optimal social trust path
selection problem is modeled as the classical Multi-Constrained Optimal
Path (MCOP) selection problem, which is proved to be NP-Complete in
[67].
(b) To address the NP-Complete social trust path selection problem, we pro-
pose an efficient approximation algorithm, MONTE K, based on the Monte
Carlo method [43], and two heuristic algorithms, H OSTP and MFPB-
HOSTP based on the Dijkstra’s shortest path algorithm [31] and our pro-
posed novel search strategies for optimal social trust path selection.
In addition, people are willing to believe what they have been told most
often by others [68]. Therefore, in order to obtain a more reasonable trust
evaluation result of a target participant, a source participant may refer to
multiple social trust paths. We propose a new efficient Heuristic algorithm
for the K Optimal Social Trust Path selection, called H-OSTP-K to select
the top K trustworthy social trust paths in a large-scale trust-oriented social
network. Experiments conducted on real online social network datasets
demonstrate the superior performance of our proposed algorithms over the
existing ones.
3. The third contribution of this thesis is a new model of trust transitivity in trust-
oriented contextual OSNs.
(a) We propose a general concept, Quality of Trust Transitivity (QoTT), to
illustrate the ability of a social trust path to guarantee a certain level of
quality in trust transitivity.
§1.3 Roadmap of the Thesis 9
(b) Based on the properties of trust illustrated in social psychology, we then
propose a new Multiple QoTT Constrained Trust Transitivity (MQCTT)
model.
Experiments conducted on real social network datasets demonstrate that
the proposed trust transitivity model follows both the principles in social
psychology and the properties of trust, and thus it obtains more reasonable
trust values than existing methods.
1.3 Roadmap of the Thesis
This thesis is structured as follows.
Chapter 2 provides a comprehensive literature review of trust, social network prop-
erties and trust management in OSNs.
Chapter 3 proposes a complex trust-oriented social network structure that contains
more social information that has significant influence on trust management. This struc-
ture can reflect the social networks in the real world better. This chapter is based on
the paper published at AAMAS 2010 [80] 1.
Chapter 4 proposes a new concept Quality of Trust Network (QoTN). In addi-
tion, to solve the NP-Complete QoTN constrained trust network extraction problem,
we propose an approximation algorithm called SCAN, and two heuristic algorithms,
SCAN-K and H-SCAN-K. Experiments conducted on real social network datasets il-
lustrate that the proposed methods can deliver high quality trust networks in less exe-
cution time than the existing methods. This chapter is based on the papers published
in AAAI 2012 and IEEE ICWS 2012 [81, 85].
Chapter 5 proposes a new general concept of Quality of Trust (QoT). In addition,
to solve the NP-Complete QoT constrained optimal social trust path selection prob-
lem, we propose an approximation algorithm, MONTE K based on the Monte Carlo
method [43], and two heuristic algorithms, H OSTP and MFPH-HOSTP, based on
1For details of the publication, please refer to page ix.
10 Introduction
Dijkstra’s shortest path algorithm [31] and our novel heuristic search strategies. Ex-
periments conducted on real social network datasets illustrate the proposed algorithms
outperform the existing methods in both the quality of the identified social trust path
and the execution time. The chapter is based on the papers published in AAAI 2010
and IEEE SCC 2010, and the paper accepted by IEEE Transactions on Services Com-
puting in 2011 [78, 83, 84, 86].
Chapter 6 proposes a heuristic algorithm, H-OSTP-K, based on Dijkstra’s shortest
path algorithm [31] and our novel heuristic search strategies for the NP-Complete QoT
constrained K optimal social trust paths selection. Experiments conducted on real
social network datasets illustrate that the proposed algorithm outperforms the existing
methods in both the quality of the identified K social trust paths and the execution
time. The chapter is based on the paper published in ICWS 2011 [85].
Chapter 7 proposes a new concept Quality of Trust Transitivity (QoTT), and pro-
poses a Multiple QoTT Constrained Trust Transitivity (MQCTT) model. The exper-
imental results demonstrate that the proposed MQCTT model follows the properties
of trust and the principles illustrated in social psychology, and thus can compute more
reasonable trust values than the existing methods that consider neither the impact of
social information nor the properties of trust in trust transitivity. The chapter is based
on the paper published in AAAI 2011 [82].
Finally, Chapter 8 concludes the work in this thesis and discusses some directions
for future research opportunities.
Chapter 2
Literature Review
Online Social Networks (OSNs) are becoming more and more popular, and have been
used as a means for a variety of activities, where trust between participants has sig-
nificant influence on their decision-making. In the literature, many scholars in both
Social Psychology and Computer Science have studied 1) social network properties,
2) trust properties, and 3) trust evaluation and trust propagation methods in OSNs. In
this chapter, we review the literature on the above three aspects organized as follows:
• Section 2.1 introduces the social network properties, and presents a new cate-
gorisation of OSNs.
• Section 2.2 introduces the different definitions of trust, the general trust proper-
ties and the influence of trust on human communities.
• Section 2.3 introduces the existing studies on different aspects of trust in OSNs,
including trust evaluation, trust network extraction, trust path selection and trust
transitivity.
2.1 Online Social Networks (OSNs)
According to the description of a social network in the discipline of Social Science
[127], a social network is a social structure made up of a set of actors (such as indi-
viduals or organizations) and the dyadic ties between these actors. The social network
perspective provides a clear way of analyzing the structure of whole social entities.
11
12 Literature Review
In this section, social network properties and a new categorisation of OSNs will be
introduced.
2.1.1 Social Network Properties
The studies of social network properties can be traced back to 1960’s when the small-
world characteristic in social networks was validated by Milgram [101], through illus-
trating that the average path length between two Americans was about 6 hops in an
experiment of mail sending. In addition, the influences of small-world characteristic
on human interactions was further analyzed by Pool et al. [110] in the 1970’s.
Associativity is a bias in favor of connections between network nodes with similar
characteristics [105]. Mcpherson et al., [98] validated the associativity characteristic
in social networks. Namely, in social networks, individuals commonly choose to asso-
ciate with others of similar age, nationality, location, race, income, educational level,
religion, or language as themselves.
In graph theory, a clustering coefficient is a measure of the degree to which nodes in
a graph tend to cluster together. Namely, in a network with a high clustering coefficient
if A has a connection with B and C, then the probability that B has a connection with
C is high. In general, a social network has a high clustering coefficient. Namely,
most of the people we know may also know one another in the social network of the
real-world scenarios, which has been validated by [55].
In recent years, as online social networks have been gaining more popularity, so-
ciologists and computer scientists have started to investigate their characteristics. In
[103], Mislove et al. analyzed several popular social networks including Facebook1,
MySpace2 and Flickr3, and validated the small-world and power-law characteristics
(i.e., in a social network, the probability that a node has degree k is proportional to
k−r, r > 1) of online social networks using data mining techniques. Also using data
1http://www.facebook.com2http://www.myspace.com3http://www.flickr.com
§2.1 Online Social Networks (OSNs) 13
mining techniques, Mccallum et al. [96] discovered the social roles (e.g., a chief
financial officer or in-house lawyer) and social relationships (e.g., partnership in a
funding application) in an email based online social network of Enron Corporation
(cs.cmu.edu/enron/). Guo et al. [52], further analyzed the influence of social interac-
tions between buyers on the purchase decisions made by a buyer in buying products in
online shopping websites.
2.1.2 The New Categorisation of OSNs
In the discipline of Computer Science, there is not any unified definition of what is
an online social network. Golbeck et al. [48] propose the criteria of Web-Based So-
cial Networks (WBSNs) as follows: 1) WBSNs could be accessible over the web
with a web browser; 2) Users of WBSNs must explicitly state their relationships with
other people; 3) The WBSN system has explicit built-in support for users to make so-
cial connections, and 4) Each relationship is visible and browseable to users. Boyd
et al. [14] propose the definition of social networking sites as “Web-based services
that allow individuals to 1) construct public or semi-public profiles within a bounded
system; 2) articulate a list of other users with whom they share connections; and 3)
view and traverse their list of connections and those made by others with the system”.
Clearly, Facebook (facebook.com) and MySpace (myspace.com) are in accordance
with these definitions. However, many other Websites, like YouTube (youtube.com),
eBay (ebay.com), Blogs and online forums, where people can share their experience
and carry out business do not follow these criteria. The relationships between partici-
pants on this type of Websites are implicit. Thus, it is still a puzzling problem whether
these Websites belong to the scope of WBSNs. Below, based on different socialities
of the participants in OSNs, a new categorisation of OSNs is introduced as below.
14 Literature Review
2.1.2.1 The Current Generation of Functional Websites
The current generation of functional websites, like eBay (ebay.com), support rich func-
tionality but not contain explicit social relationships. For example, eBay supports e-
commerce activities and buying-selling relations, however, it does not care about social
relationships like a supervisor and his/her students, and a father and his son among the
set of buyers and sellers. We summarize the characteristics of these functional web-
sites as follows.
1. They have weak sociality where the relationships between participants are im-
plicit; and participants do not keep their friendship lists and thus they can not
make new friends with friends of friends.
2. They have rich functionality, such as email, blogs, e-commerce, and video and
photo sharing etc.
2.1.2.2 The Current Generation of OSNs
As the sociality of the above websites is too weak for people to make rich social
interactions, the current generation of OSNs, such as MySpace and Facebook, emerged
in 2003 and 2005 respectively. They can explicitly express simple social relations, but
the functionality is still limited to a very small scope, like information sharing. We
summarize the characteristics of the current generation of OSNs as below.
1. They have medium sociality where the social relationships between participants
are explicit and binary (friendship or non-friendship) which can be specified
by participants; and participants can make new friends with a friend’s friends,
which is stronger than that of current functional websites.
2. They provide a platform where participants can make new friends and conduct
some simple activities (e.g., sharing photos and videos) that are not as rich as
those in current functional websites.
§2.2 What is Trust? 15
2.1.2.3 The Future Generation of OSNs based Functional Websites
We can envisage that in the near future social networks can provide the backbone to
extend a number of traditional systems. For example, a traditional e-commerce system
can have a social network of its buyers, and the friends’ friends of buyers. Likewise,
the traditional CRM (Customer Relation Management) systems can be extended to be
supported by a social network of customers and other people with relations to these
customers. Thus, the new generation of social network systems can be expected to
support both rich social relations and rich functionality. In these systems, it would be
easier to introduce products (e.g., by a retailer) or good sellers (e.g., by a buyer) to
buyers, and the friends’ friends of buyers. We summarize the characteristics of the
new generation of OSNs based functional websites as below.
1. They have strong sociality where the social relationships are explicit and com-
plex rather than binary (friendship or non-friendship) as in current generation
OSNs.
2. They provide a platform where participants can conduct rich activities, such as,
e-commerce, CRM system, recommendation systems.
2.2 What is Trust?
The Oxford Reference Dictionary (oxfordreference.com) states that trust is “the firm
belief in the reliability or truth or strength of an entity”. Based on the definition, a
trustworthy entity will typically have a high reliability, and a trustworthy person will
tell the truth and be honest with respect to interactions.
Actually, trust is a complex subject that relates to different aspects of elements,
such as belief in honesty, truthfulness, competence, and reliability of the trusted per-
son or services. In human society, trust depends on many factors, such as the past
experiences with a person, the experiences with the friends of the person, preference
to trust that is linked to psychological factors impacted by a lifetime of history and
16 Literature Review
events rumor, and the benefit by establishing the trust [66, 111]. As there are complex
factors behind a trust relation, there is no consensus definition in the literature on what
trust is [66, 111], and trust cannot be easily modeled in a computational system [48].
In this section, the trust definitions based on different aspects of views, general trust
properties, and the influence of trust on human activities will be introduced.
2.2.1 Definitions of Trust
Trust plays a role across many disciplines, including sociology, psychology, eco-
nomics, political science, history, philosophy, and computer science. Thus, there is
not a uniform definition of trust. The work in each discipline has attempted to define
the concept. In the literature, trust has been defined in many ways, as described below.
From the perspective of social psychology, Deutsch [29] proposed a widely used
trust definition. He states that trusting behavior occurs when a person encounters a
situation where he/she perceives an ambiguous path. The result of following the path
can be good or bad, and the occurrence of the good or bad result is contingent on
the action of another person. In addition, the negative impact of the bad result is
greater than the positive impact of the good result. Based on Deutsch’s definition,
Sztompka [122] proposed a general definition of trust as “Trust is a bet about the future
contingent actions of others.” There are two main components of this definition: belief
and commitment. First, a person believes that the trusted person will act in a certain
way. The belief alone, however, is not enough to say there is trust. Trust occurs when
that belief is used as the foundation for making a commitment to a particular action.
These two components are also present in the core of Deutsch’s definition: a person
will commit to take the ambiguous path if he/she believes that the trusted target person
will take the action that will lead to a good outcome.
From the perspective of sociology and history, Seligman [120] proposed a trust
definition as “trust enters into social interaction in the interstices of systems, when for
one reason or another systematically defined role expectations are no longer viable. If
§2.2 What is Trust? 17
people play their roles according to role expectations, we can safely conduct our own
transaction accordingly”. The problem of trust (distrust) emerges only in cases where
there is “role negotiability”, i.e., there is a gap between roles and role expectations
[120]. In the study of Online Social Networks, Golbeck et al. [48] defined trust as
“trust in a person is a commitment to an action based on a belief that the future action
of that person will lead to a good outcome”. This view of trust is similar with the above
definitions given by Deutsch and Sztompka respectively, as they all regard “belief” and
“commitment” as two main components of trust.
From the perspective of economics, the European Commission Joint Research
Centre [59] defined trust as “Trust is the property of a business relationship, such
that reliance can be placed on the business partners and the business transactions de-
veloped with them”. This view of trust is from a business management perspective,
which illustrates what must be done to enable trust in business. In economics trust is
often conceptualized as reliability in transactions [92].
Based on the above different trust definitions, we can see that trust is really a
composition of many different attributes, including reliability, dependability, honesty,
truthfulness, security, competence, and timeliness, which depends on the environment
in which trust is being specified.
2.2.2 Properties of Trust
Having reviewed the definitions of trust, this section introduces the general trust prop-
erties. These properties were indicated by social scientists based on their long-term
observations of large amounts of human activities. Thus, they are significant in the
study of trust management.
2.2.2.1 Context Dependency
Oxford Reference Dictionary (oxfordreference.com) states that “Context is the circum-
stances that form the setting for an event, statement, or idea, and in terms of which it
18 Literature Review
can be fully understood”. This is a general definition, where all the information re-
lated to the circumstances of an entity is regarded as the context. More specifically,
in Computer Science, a widely accepted definition was proposed by Dey et al., [30]
as “Context is any information that can be used to characterize the situation of an en-
tity. An entity is a person, place or object that is considered relevant to the interaction
between a user and an application, including the user and the application themselves.”
As indicated in Social Psychology [106], trust is highly context dependent. In
a society, a person’s trust in another person varies with the changes in contexts, as
a recommender may have a different level of expertise in different domains [3, 126].
McKnight et al. [97] have proposed interpersonal and personal trust as one of topolog-
ical categories on trust, namely, one person trusts another person in a specific context.
For example, Alice may trust Bob as a mechanic in the specific context of servicing
her car but probably not in the context of babysitting her children. Similarly, in the
discipline of Computer Science, Marsh [93] is the pioneer to propose the concept of
situational trust, which is described in an example as “Whilst I may trust my brother to
drive me to the airport, I most certainly would not trust him to fly the plane”. Namely,
the same person, but in a different context, will require different considerations with
regard to trust.
Therefore, the calculation of trust needs to consider the contextual information that
has significant influence on trust evaluation.
In OSNs, social contexts include social relationships (e.g., the relationship between
a father and his son), social positions (e.g., a professor in the data mining research
area), preferences (e.g., like play badminton) and residential locations (e.g., living in
Sydney, Australia) etc [85]. As indicated in Social Psychology [3, 76, 102], these
social contexts have significant influence on trust evaluation in OSNs.
Although it is difficult to build up comprehensive social relationships, social posi-
tions, preferences and residential locations in all domains, it is feasible to build them
up in some specific social communities by using data mining techniques. For example,
in the email based social networks (i.e., a network is formed email communication be-
§2.2 What is Trust? 19
tween participants), through mining the subjects and contents of the emails in Enron
Corporation (cs.cmu.edu/enron/), the social relationship between each pair of email
sender and receiver (e.g., a CEO and his/her assistant) can be discovered and their
roles can be known [96]. In addition, in the academic social networks formed by large
databases of Computer Science literature, the social relationships between scholars
(e.g., co-authors, a supervisor and his/her students) can be mined from publications
(e.g., from those listed on DBLP) and the role of a scholar (e.g., a professor in the field
of data mining) can be mined from their homepages [123]. Furthermore, on Facebook
(www.facebook.com), the preference and the residential location of a participant can
be mined from their profiles [103].
In addition to mining the social relationships and social roles, these values could be
explicitly specified by participants when they join in some OSNs. For example, regard-
ing the community impact factor, at LinkedIn (www.linkedin.com), a user can specify
his/her social positions (e.g., a senior C++ programmer at IBM). If the user becomes a
recommender, this social position information can illustrate his/her community impact
factor in the recommendation of a specified domain. In another example of a social
network consisting of the staff members in a University [130], the social positions of
a user can also be specified, illustrating the user’s community impact factor in the rec-
ommendations or collaborations of a specific domain. Furthermore, at SmallBlue [77],
an online social network created for IBM staff, the social position of each of the par-
ticipants (e.g. a project manager or a senior PHP developer) can be explicitly specified
when he/she joins into this social network.
2.2.2.2 Personalization
As illustrated in Social Psychology [54, 91], trust is a subjective phenomenon that is
defined by the psychological experiences of the individual who bestows it, reflecting
subjective attitudes that affect participants’ thinking based on subjective evaluation
criteria that can vary in different domains. Trust is inherently a personal opinion. Two
people often have very different opinions about the trustworthiness of the same person.
20 Literature Review
For example, suppose that Alice and Bob are two customers and Cathy is a travel
agent. Alice can trust Cathy and Bob can distrust Cathy based on their different per-
sonal preference of the services provided by Cathy and their different trust evaluation
criteria. Another good example given by Golbeck [48] is from the United States; when
asked, “do you trust the current President to effectively lead the country?” the popula-
tion will be split; some will trust him very highly, and the others will have very little
trust in his abilities.
Therefore, people can have a conflict of interests, priorities, opinions, and different
trust criteria in different domains [48]. So when and how much we trust people will
vary. Namely, there is not a universal measure of the trustworthiness of a person. In
trust calculations, the individuals personalization should be considered to reflect their
interests and opinions.
2.2.2.3 Asymmetry
Trust asymmetry, means trust is not necessarily the same in both directions between
two users. Since individuals have different experiences, psychological backgrounds,
and histories, it is understandable why two people may trust each other by different
amounts.
Trust is mutual in that each party has some trust for the other. But in real communi-
ties, there are often differences in how much they trust one another [54]. For example,
Alan trusts his manager Billy, but Billy may not trust Alan to the same degree of trust.
This is shown as a directed arrow from one user or node to another in a trust diagram
to indicate the direction of trust so that we know we are referring to the trust from Alan
to Billy, or from Billy to Alan. Another example is that research students usually say
they trust their supervisors more than the supervisors trust them. This can be seen in a
variety of hierarchies [132].
This phenomenon is called “one-way trust” [25, 54]. Namely, under certain cir-
cumstances, one person may trust the other, but there is no reciprocal trust. This
feature of trust should be considered in trust evaluation.
§2.2 What is Trust? 21
2.2.2.4 Transitivity
Trust transitivity means, for example, that if Alice trusts Bob who trusts Eric, then
Alice will also trust Eric to some extent. This assumes that Bob actually tells Alice that
he trusts Eric, which is called a recommendation [23]. Trust is not perfectly transitive
in the mathematical sense. Namely, if Alice highly trusts Bob, and Bob highly trusts
Eric, it does not always and exactly follow that Alice will highly trust Eric. Generally,
when encountering an unknown person, it is common for people to ask trusted friends
for opinions about how much to trust this new person [48]. In trust transitivity, trust
decays with the increase of transitivity hops along a social trust path [23]. The general
decay of trust is nonlinear [62, 91] and can be divided into three phases.
1. Phase 1: (Slow Decay Phase) In this phase, trust decays slowly in transitivity
along a social trust path from a source participant within a certain number of
hops. This is because the source participant may consider the familiarity with
the trustee to extend no more than a certain number of transitivity hops.
2. Phase 2: (Fast Decay Phase) With the increase of transitivity hops, the trust
decay speed increases in trust transitivity until the trust value approaches the
minimum. This is because that in this phase, the trustee is becoming stranger to
the source participant than the case in Phase 1.
3. Phase 3: When the trust value between the source participant and the trustee is
approaching the minimum, the trust decay speed changes from fast to slow. This
is because in this phase, the trustee has become a complete stranger to the source
participant.
In addition, trust transitivity needs certain constraints of context [23, 63]. For
example, if Alice trusts Bob in the domain of teaching C++, and Bob trusts Eric in the
domain of repairing a car, then the trust can not be transitive from Alice to Eric via
Bob in the domain of teaching C++. However, if Alice also trusts Bob in repairing a
car (in the same domain with Bob trusts Eric), then trust can be transitive from Alice
22 Literature Review
to Eric in this domain. This same argument can be extended to longer chains (social
trust path) of trust.
2.2.3 The Influence of Trust on Human Activities
Trust has been an important element in interpersonal relationships in many fields rec-
ognized by many research scientists. As illustrated in Social Science [25, 41, 42],
both functioning societies and online communities rely heavily on trust among their
members.
Organizations increasingly are recognizing the importance of trust in the work-
place. Trust is considered a fundamental ingredient for motivating productive working
relationships and driving a competitive business advantage [15, 115, 128]. For exam-
ple, trust facilitates strategic collaboration and cooperation [32], citizenship behavior
[28, 65, 95], and conflict resolution [107]. Trust also is related to employee attitudes,
such as job satisfaction [4, 114] and organizational commitment [25], as well as crite-
rion measures, such as justice perceptions [17] and customer satisfaction [22, 121].
As indicated in social psychology [9, 38], in the reality of our society, a person
prefers the recommendations from his/her trusted friends to those from others. In
addition, in the discipline of Computer Science, based on statistics, Bedi et al., [8]
has demonstrated that given a choice between recommendations from trusted friends
and those from recommender systems, trusted friends’ recommendations are preferred
in terms of quality and usefulness. Furthermore, in several recent studies, some re-
searchers [21, 26] have investigated how and to what extent a participant’s service
selection behavior (e.g., installing a specific application software) impacts on his/her
friends’ decision-making in service selection. These studies have indicated that the
recommendations from trusted friends have significant influence on service or target
selection, not only in the society in the real world, but also in online social networks.
Although a complete social network based trust-oriented service recommendation
system does not yet exist, it has become an important research topic in recent years.
§2.3 Trust Related Issues in OSNs 23
Some researchers [52, 90] have proposed several models to provide more accurate rec-
ommendations of products and/or services by taking some social context information
into consideration. In these studies, social trust network extraction, social trust path
selection and trust transitivity are critical problems.
2.3 Trust Related Issues in OSNs
In a social network of real-world scenarios, people conduct lots of different activities
where two persons may have no previous interactions and they do not know each other.
In such a situation, as introduced above, trust becomes one of the most important
indications for people’s decision making to guide their activities. The same situation
also happens in OSNs as the online social networking platforms have also been used
for a variety of activities, e.g., employment, recommendation system, CRM system
etc. Therefore, it is necessary and significant to evaluate trust between two unknown
participants in OSNs. As trust management is a significant research area in OSNs,
in the literature, many trust models and trust evaluation methods have been proposed
in the study of OSNs. Based on the different aspect of trust problems they addressed,
these existing works can be divided into the categories of as 1) trust evaluation, 2) trust
network extraction, 3) trust path selection, and 4) trust transitivity.
2.3.1 Trust Evaluation in OSNs
Trust is a critical factor in the decision-making of participants in online social networks
[71]. In order to evaluate the trust between two unknown participants in OSNs, in this
field, several trust management methods have been proposed.
In the studies of trust propagation, Golback et al. [47] firstly extended the Friend
of A Friend (FOAF) vocabulary (foaf-project.org) by adding a property where users
can specify how much they trust one another based on their past interactions. The new
feature has been adopted on FilmTrust, where a participant can specify a trust rating
24 Literature Review
that range from 1 (very little trust) to 10 (very high trust) to another participants based
on the quality of the participant’s movie recommendation. Then, they proposed a trust
inference mechanism for establishing the trust relation between a source participant
and the target one who have no direct interactions [48]. In their model, the attitudes
of those neighbors that have been trusted by the source (have been given a high trust
value by the source) are considered in the computation of the inferred trust values of
those nodes which are neighbors of those neighboring nodes. Their model averages
those trust values given by the neighbors of the source to their neighbors and this pro-
cess will be repeated till the target node. This trust inference model has also been
further adopted into FilmTrust. Guha et al. [51] proposed a trust propagation model
to infer trust and distrust between two participants who have no direct interactions. In
their model, the number of propagation hops, and the trust situations of the interme-
diate nodes in the social trust paths between the source and the target are considered.
They adopted a weighted sum method to aggregate each of the above parts that have
influence on trust propagation to compute the inferred trust value.
In the studies of trust-oriented recommendation systems, Walter et al. [124] pro-
posed a recommendation system in a social network. In their model, a participant can
give a trust value to a recommender based on the recommendation behavior of par-
ticipants. This trust value is visible and regarded as a reference for other participants
to select recommendations. The participants compute the trust value of a target par-
ticipant based on multiplying the trust value between any intermediate participants in
the social trust paths between a source and the target. Jamali et al. [58] proposed
a random walk model in an OSN consisting of sellers and buyers. In their model, a
buyer performs several random walks with a fixed number of hops along a path from
this buyer in the social network to find the ratings given by the ending participant to
a seller who sells products preferred by the buyer. The degree of confidence on the
seller is calculated based on the number of random walk paths, hops and ratings of the
seller in each path.
The above trust evaluation methods consider the trust values between intermedi-
§2.3 Trust Related Issues in OSNs 25
ate nodes in the social trust paths, which can help establish trust relation between
two unknown participants. However, all the above strategies are solely based on trust
values given by participants. The social context including social relationships (e.g.,
the relationship between a buyer and a seller, or the one between an employer and
an employee), social positions (e.g., the supervisor as a referee in a job application)
and preference (e.g., like playing badminton) are not taken into account in these trust
evaluation methods. As pointed out in Social Science theories [3, 102, 76], such social
information has significant influence on trust evaluation, and can impact on partici-
pants’ decision-making. Thus, the existing methods cannot be expected to deliver a
reasonable trust evaluation result without considering social information.
2.3.2 Trust Network Extraction in OSNs
Participants usually have interactions with each other and they give trust ratings (val-
ues) to each other based on their interactions. Then a trust network from a source to a
target (e.g., the trust network from A to E in Fig. 1.1 in Chapter 1) can be formed. The
trust network contains some important intermediate participants, the trust relations be-
tween them and the social context underlying their past interactions. This information
has important influences on trust relationships and trust evaluation. Thus, the trust
network provides a basis for evaluating the trustworthiness of the target.
Section 2.3.1 has introduced some existing trust evaluation approaches that eval-
uate the trust value between any two nonadjacent participants. However, these meth-
ods all assume the trust network between the two participants have been identified
[48, 79, 83] as the basis of their trust evaluation models. Namely, extracting such
a contextual trust network between two nonadjacent participants is an essential step
before performing any trust evaluation between them.
In the graph formed by social interactions, cycles (e.g., A → B → C → A in Fig.
1.1) usually exist due to the interactions among multiple participants [103]. Extracting
a sub network from a cyclic network has been proved to be an NP-Complete problem
26 Literature Review
[6]. To the best of our knowledge, there are no approximation algorithms proposed
for the NP-Complete trust network extraction in OSNs in the literature. However, the
resource discovery problem in P2P networks has similar properties as the trust network
extraction problem. Thus, some search strategies have been developed for the resource
discovery problem and they can be applied in trust network extraction. These strategies
can be classified into the following three categories.
2.3.2.1 Flooding-Based Search (FBS)
The Flooding-Based Search (FBS) mechanism typically searches the network from
the source by using the Breadth First Search (BFS) strategy to find the target resource
in a P2P network. It has been applied into Gnutella (rfc-gnutella.sourceforge.net),
a large P2P network where individuals can exchange files over the Internet directly
without going through a Web site (e.g. it has been used as a means to download music
files from or share them with other Internet users). FBS sends a query of finding the
target resource to each of the neighboring nodes in the network, which can make FBS
method inherently unscalable in a large-scale network. As the large amount of queries
FBS forwarded can consume huge computation time, the Time To Live Breadth First
Search (TTL-BFS) method [19, 37] was proposed. In TTL-BFS, the Time To Live
(TTL) is usually set to be an integer to indicate the time of the BFS. During TTL-
BFS, TTL value is decreased by 1 or V r (0 < V r < 1) when the depth of search
is increased by 1. In this process, if the target resource is found, then the search
terminates. Otherwise, TTL-BFS continues with BFS till TTL = 0.
2.3.2.2 Random Walk Search (RWS)
A Random Walk is a mathematical formalization of a path that consists of a succession
of random steps. Random Walk Search (RWS) is a popular alternative to FBS for
locating resources in P2P networks [45, 46].
In RWS, firstly, the source node is regarded as the “querying” node that needs to
§2.3 Trust Related Issues in OSNs 27
locate a resource. The querying node randomly selects up to K (K is no greater than
the number of the querying node’s neighbors) neighboring nodes to send queries. Each
of these K queries is called a random walker. Each random walker has a time to live
(TTL) value that is initiated with some value T > 0 that limits the number of times the
random walker is forwarded. When an intermediate node receives a random walker, it
checks to see if it has the resource. If the intermediate node does not have the resource,
it checks the TTL value, and if T > 0, it decrements T by 1 and forwards the query to
a randomly chosen neighbor, otherwise, if T = 0 the query is not forwarded and RWS
terminates. On the other hand, if the intermediate node has the resource, the query is
not forwarded and a reply is sent to the querying node.
2.3.2.3 High Degree Search (HDS)
In High Degree Search (HDS) [2], firstly, the source node sends a query to all its
neighbors based on the BFS method to determine whether they contain the resources
or not. If none of the neighbors contains the resources, then HDS broadcasts the search
messages along directions of the nodes with the highest degree according to the DFS
method, and sets the state of the node to indicate the node has been accessed. If it does
not find the resource along directions of the nodes with the highest degree, the search
message will return the precursor node and broadcast along its neighbor node with the
second highest degree. This procedure will stop until the search steps increase to a
predefined threshold or all the nodes in the network have been accessed. In extreme
cases, when the outdegree of the node are all the same, the algorithm degenerates into
the standard BFS algorithm. When all the outdegree of the node are different, the
algorithm degenerates into the standard DFS algorithm.
Analysis: The above search methods have been validated in many P2P networks
and they have good performance in resource discovery in P2P networks. However, P2P
networks do not contain social contextual information, including social relationship,
social position and preference, etc. Thus, these existing methods do not consider the
social context in target resource discovery but the social context has a significant in-
28 Literature Review
fluence on social interactions and trust evaluation in OSNs. In addition, as introduced
in Section 2.3.1, different people may have different trust evaluation criteria, and thus
the trust evaluation criteria specification should be considered in trust network extrac-
tion. But this feature is not supported by these existing methods for resource discovery
in P2P networks. Thus, these existing methods cannot be expected to extract a high
quality trust network to deliver a trustworthy trust evaluation result.
2.3.3 Trust Path Selection in OSNs
As shown in Fig. 1.1, a trust network can contain many social trust paths (e.g., path
A → B → C → E and path A → B → D → E). Evaluating trust based on all the
social trust paths in a trust network can lead to huge computation time, which makes
it inapplicable in large-scale social networks. In the literature, a few works have been
proposed to address the social path selection problem in such networks.
SmallBlue [77] is an OSN created for IBM staff. It also provides information an-
laytics services that automatically visualizes social networks, helps participants man-
age and expand their social capital, and enables participants to find people with spe-
cific knowledge. In this system, if a source would like to find a target (e.g., a C++
programmer), it considers up to 16 social paths between them with the path length of
no more than 6 hops, among which, the shortest one is taken as the optimal path. In
this method the shortest path can mostly affect the decision-making of the source. But
the trust situation between the intermediate nodes in a social path is neglected which
has significant influence on participants decision making. Hang et al. [53] proposed a
social trust path selection method in online social networks, where trust between par-
ticipants is considered in the path selection. In their model, the aggregated belief value
(trust value) of a social trust path is computed by multiplying the trust value between
any two intermediate nodes in the path. Among all the social trust paths, the one with
the highest aggregated belief (i.e., the maximum of aggregated trust value) is selected
as the optimal path that yields the most trustworthy result of trust propagation between
§2.3 Trust Related Issues in OSNs 29
a source participant and the target participant. This model considers trust information,
but does not have any concern for participants different trust evaluation criteria. Wang
et al. [125] proposed a social trust path selection method where a source participant
can specify a threshold. Their method first aggregated trust values given to each of
the recommenders (i.e., the intermediate nodes) in the network between a source par-
ticipant and the target participant. If the aggregated trust value of a recommender is
greater than the threshold specified by the source participant, the recommender is kept
in the trust network. Otherwise, the recommender (the node) is deleted from the trust
network. After this process of node deletion, the rest of the social trust paths are kept
for trust evaluation.
These existing methods select the optimal social trust path(s) from a large volume
of paths based on different selection criteria, which indeed reduces the computation
complexity of the trust evaluation between two unknown participants. However, in
the above methods, the social information including social relation, social position
and preference of participants are not taken into account in path selection. In addi-
tion, a source participant can have different purposes in evaluating the trustworthiness
of the target participants (e.g., employment or buying products). Their different trust
evaluation criteria in different applications should be reflected by specifying certain
constraints of the above social information for social trust path selection. Thus, al-
though trust information is taken into consideration in some of the existing trust path
selection methods, they cannot be expected to select the trustworthy trust paths without
considering social information and complex trust criteria specification.
2.3.4 Trust Transitivity in OSNs
The trust transitivity property has been validated in both Social Psychology [23] and
Computer Science [63, 48]. As introduced in Section 2.2.2, under the same context,
if A trusts B and B trusts C, then A can trust C to some extent. For example, Alice
needs to have her car serviced, and she asks Bob for his advice about where to find a
30 Literature Review
good car mechanic in town. Bob is thus trusted by Alice to know a good car mechanic
and to tell his honest opinion about that, where as Bob actually trusts the car mechanic.
After extracting the trust network and finding those trustworthy social trust paths
from the trust network, to deliver a reasonable trust value in the trust management
of OSNs, we need to know how trust is transitive along a social trust path. As this
is a significant and challenging problem in the study of trust in OSNs, some trust
transitivity models in OSNs have been proposed in the literature, and these existing
models can be classified into three categories based on the types of trust transitivity
strategies they adopted. These strategies are 1) multiplication strategy, 2) averaging
strategy, and 3) confidence-based strategy. This section discusses each strategy and
analysis the disadvantages of the existing models.
In the first category, the trustworthiness of a target participant is computed as
the multiplication of the trust values between any two adjacent participants along a
social trust path. For example, if A trusts B with TAB and B trusts C with TBC
(TAB, TBC ∈ [0, 1]), then A trusts C with TAC = TAB ∗ TBC . This strategy has been
used in many existing models. For example, Walter et al., [124] proposed a social
network based recommendation system, where they adopted this type of a trust transi-
tivity model to compute the trustworthiness of a target recommender along the social
trust path from a recommendee to the recommender. In addition, Lei et al., [73] pro-
posed a composite service trust evaluation method, where they adopted this type of
trust transitivity model to compute the aggregated trust value of a composite service
along a service composition path.
In the second category, the trustworthiness of a target participant is computed
based on averaging the trust values between any two adjacent participants along a
social trust path. i.e., TAC = (wi · TAB + wj · TBC)/2, where wi and wj are the
weights of TAB and TBC respectively, and wi + wj = 1. In the literature, Gary et
al., [50] proposed a trust-based admission control model. In their model, they adopted
this type of trust transitivity model to evaluate the trust of unknown participants and
the evaluated trust values are used to participants access control. In addition, Golbeck
§2.3 Trust Related Issues in OSNs 31
et al., [48] proposed a trust inference method, where they adopted this type of trust
transitivity model to compute the inferred trust value of the target participant. They
further adopted their trust inference model into FilmTrust.
In the third category, the confidence between participants is considered in trust
transitivity, i.e., TAC is calculated based on TAB, TBC and the confidence of A on TBC
(denoted as CA) . CA is computed based on the preference similarity between A and
B, and it is proportional to the latter. In the literature, Guha et al., [51] have proposed
a trust and distrust propagation model in OSNs. In their model, in addition to the trust
between any two intermediate participants in a social trust path, the individual trust
of each intermediate participant was also considered as the confidence in trust transi-
tivity. The confidence value was combined with the trust value between intermediate
participants by using the weighted sum method to compute the trust value of the target.
In addition, Kuter et al., [71] have proposed a trust inference model, where the con-
fidence of an intermediate participant was considered. In their model, the confidence
values were given by domain experts, and they were used in probabilistic models to
compute the probability of the trustworthiness of the target under the given confidence
values of the intermediate nodes and the confidence values of the trust between them.
These existing trust transitivity models provide some feasible methods to evaluate
the trustworthiness of the target along a social trust path. However, they have the fol-
lowing drawbacks that lead to inaccuracy and unreasonable trust values delivered by
the existing models. Firstly, they do not follow the nature of trust decay illustrated in
social psychology [44, 61]. Secondly, social psychology [3, 23] also illustrates that
trust is not transitive in all situations. For example, Alice trusts Bob (a football player)
in playing soccer and Bob trusts Tom (a car mechanic) in repairing a car. In such a
situation, Alice may not trust Tom in playing soccer. Namely, participants have dif-
ferent social positions (e.g., a football player or a car mechanic) in different domains
(e.g., playing soccer or repairing a car), which impact on trust transitivity. But ex-
isting methods do not consider this impact factor. Moreover, the social relationships
between participants have significant influence on trust transitivity [102]. However,
32 Literature Review
they are not considered in existing trust transitivity models either. Finally, a source
participant should be able to set certain constraints of the above impact factors as cri-
teria for the trust transitivity in different domains [91, 126]. But this is not supported
by existing methods.
2.4 Conclusions
This chapter has provided a general overview of the research on social networks, trust
properties and trust management in OSNs. We have first presented the social network
properties indicated by social scientists that need to be followed in trust management.
Then we have presented a new categorisation of OSNs based on their different so-
cialities. In addition, we have presented trust definitions and trust properties that are
indicated by social scientists based on their long-term observation of a large number
of human activities. Therefore, these characteristics of trust should be considered in
trust management. Furthermore, we have analysed the advantages and disadvantages
of the existing studies of different aspects of trust management in OSNs, including
trust evaluation, trust network extraction, trust path selection and trust transitivity.
Chapter 3
Contextual Trust-Oriented Social
Networks
In Chapter 1, we have introduced the existing social network structure as shown in Fig.
1.1, which only contains the trust information between two participants. However,
social networks contain complex social information, including social relationships,
social positions, residential locations and preferences. But such social information has
not been included in any existing social network structure. This chapter presents a
complex contextual trust-oriented social network structure, where not only trust but
also the complex social contextual information are taken into account in modelling,
better reflecting the social networks in reality. This structure is the basis for all the
trust management and evaluation methods proposed in this thesis.
3.1 Social Context
As illustrated in Social Science [7], social context is the social environment of individ-
uals, including the culture in which he/she was educated and/or lives in, and the peo-
ple and institutions with whom the person interacts. In Computer Science, researchers
have proposed the definitions of social context in some specific social networks. For
example, Yang et al. [131] define the social context in micro-blog systems as “com-
pared with traditional contexts that are defined based on textual information, social
context in micro-blog systems need incorporate various dynamic social relationships,
33
34 Contextual Trust-Oriented Social Networks
such as the follower-followee relationships between users, retweeting relationships
and replying relationships between tweets”. In addition, in recommender systems, Ma
et al. [89] gave the definition of social context as “social context information including
users’ social trust network, tags issued by users or information about the interests of
users or properties of items.”
In this thesis, the definition of the social context in a general social network is
proposed as below:
Definition 1: Social Context (denoted as SC) is the social environment of a partici-
pant in social networks, which is divided into the independent social environment and
the dependent social environment. Independent social environment contains the inde-
pendent social properties associated with one person, like social position, residential
location, and preference. Dependent social environment includes the social relation-
ship between participants, the indegree and outdegree of a participant.
3.1.1 Independent Social Environments
3.1.1.1 Social Position
Social position is the position of an individual in a given community and culture. A
person can have several social positions in different domains [3]. For example, a
researcher can be a professor and the head of a department in a university. Let SPDiA
denote A’s social position in domain i.
3.1.1.2 Preference
In Social Psychology [75], preferences could be conceived of as an individual’s atti-
tude towards a set of objects, typically reflected in an explicit decision-making pro-
cess. A person can have different preferences in different domains. For example, a
researcher prefers doing collaboration with others who have the same research inter-
ests with him/her, and the researcher may like playing badminton as well. Let PFDiA
denote A’s preference in domain i.
§3.1 Social Context 35
3.1.1.3 Residential Location
The residential locations of participants are the places where people live. Let RLA
denote the residential location where A lives.
3.1.2 Dependent Social Environments
3.1.2.1 Social Relationship
As indicated in Social Science [102], two participants can have more than one type
of social relationships. For example, A and B are colleagues. They can also be the
members of a badminton club. Let SRTYj
A,B (j ∈ [1, 2, ..., n]) denote the n types of
social relationships between participants A and B.
3.1.2.2 Indegree
In social networks, the indegree of a participant is the number of participants who have
social interactions with him/her. A large indegree of a participant in an OSN indicates
the participant is well known in the community. Moreover, the recommendation from
such a participant with a larger indegree is more credible and this has been validated
in Social Science theories [112]. Let deg−(A) denote the indegree of A.
3.1.2.3 Outdegree
In social networks, the outdegree of a participant is the number of other participants
with whom this participant has social interactions. The larger the outdegree of a par-
ticipant in an OSN, the more opportunities he/she has a social connection with others
in the community (i.e., connect with unknown participants with the direct social in-
teractions via intermediate nodes). If a node has a higher outdegree, it indicates that
the node has more neighboring nodes. Thus, it is more likely for such a node to be
connected with the target node via its neighbors and its neighbors’ of neighbors. Let
deg+(A) denote the outdegree of A.
36 Contextual Trust-Oriented Social Networks
As analysed above, let NE(A) = {B1, ..., Bn} be the set of all the neighbors of A;
then the social context of A in a social network for a given domain Di can be denoted
as SC(A) = {{SPDiA , PFDi
A , RLA, SRTYj
A,Bj, deg−(A), deg+(A)}|(Bj ∈ NE(A), j ∈
[1, 2, ..., n]}.
3.2 Social Contextual Impact Factors
As indicated in Social Psychology [3, 75, 102], social contexts have significant influ-
ence on trust evaluation. Then based on the social contexts in social environments,
several social context impact factors are proposed as follows.
3.2.1 Trust
As introduced in Section 2.2.1, trust is a complex subject, and lots of trust definitions
have been proposed in different disciplines. In this thesis, we propose the definition of
trust as below,
Definition 2: Trust is the belief of one participant in another, based on their interac-
tions, with the extent to which the future action to be performed by the latter will lead
to an expected outcome.
As pointed out in [91, 126], the trust value between two people can be different in
different domains. For example, A trusts B in teaching C++, but A may not trust B in
repairing a car. In our model, let TDiAB ∈ [0, 1] (e.g., TDi
AB = 0.5 in the closed interval
between 0 and 1) denote the trust value that A assigns to B in domain i. If TDiAB = 0,
it indicates that A completely distrusts B in domain i, while TDiAB =1 indicates that A
completely believes B’s future action can lead to the expected outcome in that domain.
3.2.2 Social Intimacy Degree
As illustrated in Social Psychology [5, 16], a participant can trust and have more so-
cial interactions with the participants with whom he/she has more intimate social re-
§3.2 Social Contextual Impact Factors 37
lationships than those with whom he/she has less intimate social relationships. Let
SIAB ∈ [0, 1] (e.g., SIAB = 0.5 in the closed interval between 0 and 1) denote the So-
cial Intimacy Degree between A and B in online social networks. SIAB =0 indicates
that A and B have no intimate social relationship while SIAB =1 indicates they have
the most intimate social relationship.
As introduced in Section 2.2.2.1, in email based social networks, through mining
the subjects and contents of the emails, such as those in Enron Corporation
(cs.cmu.edu/enron/), the social relationship between each pair of email sender and
receiver (e.g., a CEO and his/her assistant) can be discovered. In addition, in the
academic social networks formed by large databases of Computer Science literature,
the social relationships between scholars (e.g., co-authors, a supervisor and his/her
students) can be mined from their publications (e.g., from DBLP). Based on the mined
social relationships, the corresponding social intimacy degree between participants can
be computed by using probabilistic models [96] or the PageRank model [123].
3.2.3 Community Impact Factor
Rich activities of participants in social networks can be categorized into different do-
mains (e.g., hiring employees or product sales) based on their characteristics [126].
As illustrated in Social Psychology [3, 27], in a certain domain of interest, an expert’s
recommendation is more credible than that from a beginner. In addition to expertise,
as illustrated in Cognitive Science [69] and Computer Science [112], a well-known
person (i.e., a large indegree of the node) is more credible than that of a person who
is interacted by less people. Therefore, let CIFDiA ∈ [0, 1] (e.g., CIFDi
A = 0.5 in the
closed interval between 0 and 1) denote the Community Impact Factor of A, illustrat-
ing the community impact of participant A in domain i, which is determined by the
expertise of A and the number of social interactions with A (i.e., deg−(A)) in domain
i. CIFDiA =1 indicates that A is a domain expert and has the greatest impact in domain
i while CIFDiA =0 indicates that A has no knowledge and has the least impact in that
38 Contextual Trust-Oriented Social Networks
domain.
As introduced in Section 2.2.2.1, in the email based social networks, the social po-
sition, like a CEO or his/her assistant can be discovered through mining the subjects
and contents of the emails. In addition, in the academic social networks, the social
position of a scholar (e.g., a professor in the field of data mining) can also be mined
from their homepages. Then, based on mined social position information, the corre-
sponding community impact factors can also be calculated by adopting probabilistic
models [96] or PageRank model [123].
3.2.4 Preference Similarity
As illustrated in Social Psychology [88, 136], a participant A can trust and have more
social interactions with another participant B, with whom A has more similar prefer-
ences (e.g., both of them like playing badminton) than others, with whom he/she has
fewer similar preferences. Let PSDiAB ∈ [0, 1] (e.g., PSDi
AB = 0.5 in the closed inter-
val between 0 and 1) denote the Preference Similarity between A and B in domain i.
When PSDiAB =0, A and B have no similar preference in domain i. When PSDi
AB =1,
they have the same preference in that domain.
On Facebook, as the preference of a participant can be found from his/her profile,
the preference similarity between two participants can be mined based on their profiles
[103].
3.2.5 Residential Location Distance
As illustrated in Social Psychology [7, 44], a participant A can trust more on and have
more social interactions with B if A’s residential location is closer to B than others
whose residential location is far away. Let RLDAB∈ [0, 1] (e.g., RLDAB = 0.5 in the
closed interval between 0 and 1) denote the Residential Location Distance between A
and B. When RLDAB = 1, the residential locations of A and B are the same. When
RLDAB = 0, it indicates that the residential location between them has the largest
§3.3 A Contextual Trust-Oriented Social Network Structure 39
distance.
On Facebook, the residential location of a participant can also be found from
his/her profile, and then the corresponding residential location distance between two
participants can also be calculated [103]. Detailed mining methods of these social
contextual impact factor values are out of the scope of this thesis.
3.3 A Contextual Trust-Oriented Social Network Struc-
ture
A B
D
E targetsource
C
TDi
AB
TDi
BC
TDi
CE
TDi
BE
TDi
BD
TDi
DE
SIAB
SIBC
SICE
SIBE
SIBD
SIDE
PSDi
AB
PSDi
BC
PSDi
CE
PSDi
DE
PSDi
BD
RLDAB
RLDBD
RLDDE
RLDCE
RLDBC
RLDBE
PSDi
BE
CIFDi
B
CIFDi
C
CIFDi
D
Figure 3.1: A contextual trust-oriented social network
Based on the social contextual impact factors identified above, a new structure for
complex contextual trust-oriented social networks is shown in Fig. 3.1, where for each
participant (e.g., B), the community impact factor (e.g., CIFDiB ) is added, and for each
pair of participants who have direct interactions (e.g., A and B), the social intimacy
degree (e.g, SIAB), trust (e.g., TDiAB), preference similarity (e.g., PSDi
AB) and residential
location distance (e.g., RLDAB) are added.
40 Contextual Trust-Oriented Social Networks
3.4 Conclusion
In this chapter, we have introduced the social contextual information proposed to be in-
cluded in social networks. In addition, based on these social contexts, the correspond-
ing social contextual impact factors are proposed which have significant influences on
trust evaluation. Furthermore, we have proposed a complex contextual trust-oriented
social network structure, which contains the social contextual impact factors, including
social intimacy degree, community impact factor, preference similarity and residential
location distance. This structure can better reflect the social network structure in the
real-world scenarios, and thus it is proposed to be the basis to develop reasonable trust
management and evaluation models in OSNs.
Chapter 4
Trust Network Extraction in
Large-Scale Trust-Oriented Social
Networks
4.1 The Trust Network Extraction Problem
As introduced in Chapter 1, an Online Social Network (OSN) can be represented as
a graph, where each node represents a participant and each link between two nodes
corresponds to a real-world or online interaction. In the social network depicted in
Fig. 1.1, suppose A is looking for a badminton coach and E is a badminton coach. In
such a situation, as indicated in the theory of Social Psychology [23, 91] and Computer
Science [48, 78], A can evaluate the trustworthiness of E based on the trust network
from A to E by using trust transitivity and trust propagation methods [48, 78]. There-
fore, in OSNs, such a trust network is critical and the basis for the trust evaluation
for two nonadjacent participants, as it contains some important intermediate partici-
pants, the trust relations between those participants and social context. All of them
have important influences on the trust evaluation between two unknown participants
in OSNs. Extracting the trust network between two unknown participants becomes a
fundamental and essential step before performing trust propagation [48, 83, 85].
As introduced in Chapter 2.3.2, extracting a sub network from a cyclic network
has been proved to be an NP-Complete problem [6]. Therefore, in real applications,
41
42 Trust Network Extraction in Large-Scale Trust-Oriented Social Networks
A B E targetsource
C
TAB
TBC TCE
TBE
Figure 4.1: A sub trust network (TN-part-1)
A B
D
E targetsource
TAB TBE
TBD TDE
Figure 4.2: A sub trust network (TN-part-2)
only part of the trust network can be extracted for trust evaluation, which consequently
affects the reliability of trust evaluation in response to a trust query given in a certain
context.
For example, in Fig. 1.1 shown in Fig. 1, suppose C has no knowledge of bad-
minton, and personally, C does not know E well. TCE was given by C as C bought a
used car from E. But D is good at playing badminton and D is familiar with E, TDE
was given by D as D usually plays badminton with E. Fig. 4.1 and Fig. 4.2 depict
two possible sub trust networks (denoted as TN-part-1, and TN-part-2) extracted from
the whole trust network in Fig. 1.1.
In the trust query of looking for a badminton coach given by A, based on the
trust theory in Social Psychology [23, 91], D’s recommendation of E may be con-
sidered more credible than C. From the two figures, we can see that TN-part-1 does
not contain the important intermediate node D and the important trust relation TDE .
Therefore, based on the trust theory in Social Psychology [23, 91], the trust evalua-
tion result delivered based on TN-part-1 is less reasonable than that delivered based on
§4.1 The Trust Network Extraction Problem 43
TN-part-2. Namely, it is not reasonable to adopt the trust value given by a participant,
who has no knowledge about badminton, based on the sale of a used car to evalu-
ate the trustworthiness of a person to be a badminton coach. Therefore, given a trust
query under a certain context (e.g., looking for a badminton coach), a trust network
has higher quality (e.g., TN-part-2) if the network contains more important intermedi-
ate participants (e.g., D), their trust relations (e.g., TBD and TDE in Fig. 4.2) and the
corresponding contextual information (e.g., D is familiar with E and D has expertise
in the domain of playing badminton in Fig. 4.2), and excludes those less important
(irrelevant) nodes (e.g., C) and links (e.g., TCE). Such a trust network with higher
quality can deliver more reasonable trust evaluation results. Therefore, it is necessary
and important to address the challenging NP-Complete trust network extraction prob-
lem to provide a high quality trust network as the foundation for the trust evaluation
between two unknown participants.
In the literature, to the best of our knowledge, there are no proposed methods for
the NP-Complete social trust network extraction problem. But some resource dis-
covery methods, which are developed for P2P networks, can be used for trust network
extraction in OSNs, as it has similar properties as the trust network extraction problem.
Such as 1) Time To Live Breadth First Search (TTL-BFS) method [19, 37], 2) Random
Walk Search (RWS) method [45, 46], and 3) High Degree Search (HDS) method [2].
But these methods do not consider the social contexts, including social relationships,
social positions, residential locations and preferences of participants. As indicated in
Social Psychology [16, 75, 135], all the above social contextual information has sig-
nificant influence on both social interactions and trust evaluation. In addition, a source
participant may specify some constraints on social contexts to reflect his/her trust eval-
uation criteria in trust network extraction. However, it is not supported by the above
existing resource discovery methods in P2P networks.
This chapter first proposes a new concept, called QoTN (Quality of Trust Network)
and proposes a social context-aware trust network extraction method with QoTN con-
straints. Moreover, to address the NP-Complete trust network extraction problem, this
44 Trust Network Extraction in Large-Scale Trust-Oriented Social Networks
chapter then proposes an approximation algorithm, called SCAN, based on the Monte
Carlo method, and two heuristic algorithms, called H-SCAN and H-SCAN-K based on
K-Best-First Search (KBFS) method [34], bidirectional search (i.e., search from both
the source and the target nodes simultaneously) [57] and our proposed optimization
and heuristic search strategies. The experimental results illustrate that on average our
methods can extract trust networks with higher quality by consuming less execution
time than the existing methods.
4.2 Social Context-Aware Trust Network Extraction Mod-
els
In this section, we first discuss the influence of social contextual impact factors on so-
cial interactions and social connections, and then propose a new concept called Quality
of Trust Network (QoTN) and a trust network utility calculation method, all of which
are the key components of our social context based trust network extraction model.
4.2.1 The Influence of Social Context on Social Interactions and
Social Connections
In Computer Science, based on the statistics of 1000 publications from 18 countries on
ISI Web of Knowledge (apps.webofknowledge.com) [129], in 54% of the papers, the
first author and the last author had the same address. In addition, based on the statistics
on Flickr (flickr.com) - an online photo sharing social network [103], any two partic-
ipants in photo sharing usually have similar preferences. These examples illustrate
that the social context of two participants (e.g., residential location and preference)
have influence on their social interactions in different domains (e.g., in research and
in photo sharing), and thus can affect social connections between participants. This
feature also has been validated by Social Psychology theory [16, 44, 88, 136]. Next,
we give an example to illustrate the influences of social context on social connections.
§4.2 Social Context-Aware Trust Network Extraction Models 45
A C
B
targetsource
a lecturer in the Department of
Computing, Macquarie University
(MQU)
a badminton fan
a student who studies
in MQU with a major
in Computer Science
the member in a
badminton club
a badminton coach
who lives in Sydney
Figure 4.3: The influence of social context on social connections
As depicted in Fig 4.3, A is a lecturer in the Department of Computer Science of
Macquarie University in Sydney, Australia, and he/she has social interactions with B
as B is a student of A. C is a badminton coach and lives in the same city with both A
and B. B does not have direct interactions with C. In the OSN, suppose A is looking
for a badminton coach, (i.e., A is the source and C is the target), we could see that B
and C have a high probability to have a social connection as both of them like playing
badminton and thus they may be connected via some other members in a badminton
club.
From this example, we can see that the social context similarity between two un-
known participants can affect the social interactions and thus affect the probability of
their social connections. Based on this property, we can estimate a social connection
based on the social context similarity between participants. Next we propose a social
context similarity method by Eq. (4.1).
Let SmiDivm,vt
denote the social context similarity between vm and vt in domain
i (vm is nonadjacent with vt), which can be calculated by the following Eq. (4.1).
This method considers the influence of different social contexts including preference
similarity, the similarity of community impact factors and residential location distance
in different social networks.
46 Trust Network Extraction in Large-Scale Trust-Oriented Social Networks
SmiDivm,vt
=ω1 ∗ PSDivm,vt
+ω2∗|CIFDivm−CIFDi
vt|+ω3∗RLDvm,vt (4.1)
where ω1, ω2 and ω3 are the weights of social impact factors and ω1 + ω2 + ω3 = 1.
These weights can be different in different social networks. For example, in a social
community, if the preference similarity between participants has more impact on social
connection, ω1 should be given a relatively high value.
The larger the social context similarity between two participants, the more likely
for them to having social connections. In our model, the social context similarity
is considered in the node selection of trust network extraction, where the larger the
similarity between a node and the target which are nonadjacent, the more likely for
the node to be selected (e.g., B has a higher likelihood to be selected as it has similar
social context with target C in Fig. 4.3.)
4.2.2 Quality of Trust Network (QoTN)
In addition to the influence of social contexts, our model also considers different trust
evaluation criteria in trust network extraction. We first present a new concept, Quality
of Trust Network, as below.
Definition 2: Quality of Trust Network (QoTN) is the ability of a contextual
trust network to guarantee a certain level of trustworthiness in trust evaluation, tak-
ing T, SI, CIF, PS, RLD as attributes.
In our model, a source participant can specify multiple constraints of QoTN at-
tributes (i.e., T , SI , CIF , PS and RLD) for intermediate nodes and their links in
a trust network, as the requirements of trust network extraction in different domains.
Let QoTN(η)vs,vt (η ∈ {T, SI, CIF, PS, RLD}) denote the QoTN constraint of η
in the trust network from vs to vt (throughout this thesis, vs denotes the source and
vt denotes the target in a social network). For example, to hire employees, vs, a hir-
ing manager, can specify the QoTN constraints as {QoTNTvs,vt
> 0.3, QoTNSIvs,vt
>
0.3, QoTNPSvs,vt
> 0.3, QoTNRLDvs,vt
> 0.3, QoTNCIFvs,vt
> 0.8}, if he/she believes the
§4.3 The Proposed SCAN Algorithm for Trust Network Extraction 47
community impact factor of each of the intermediate participants is more important in
the domain of recruitment.
4.2.3 Trust Network Utility
In our model, we define the utility (denoted as U) as the measurement of the trustwor-
thiness of an extracted trust network. In a given domain, the utility function takes the
QoTN attributes T , SI , CIF , PS and RLD as the arguments in Eq. (4.2)
U(vs, vt) =N∑
j=1
Tj +N∑
j=1
SIj +M∑
j=1
CIFj +N∑
j=1
PSj +N∑
j=1
RLDj (4.2)
where M is the number of intermediate nodes and N is the number of corresponding
links in the trust network,
The goal of trust network extraction is to extract the optimal trust network from the
source vs to the target vt that satisfies multiple QoTN constraints and yields the highest
utility, which is an NP-Complete problem as it covers finding the longest simple path
(a simple path is an acyclic path) in a graph which has been proved to be NP-Complete
[6].
4.3 The Proposed SCAN Algorithm for Trust Network
Extraction
4.3.0.1 Social Context-Aware Social Interaction Probability
In the real world, the normal distribution has been widely used since the 18th century
to model the relative frequency of physical and social phenomena [60], for example,
the IQ, income and reading skills of people in a general population, the box-office per-
formance of feature films, the output of journal articles by scientists, and the number
of violent acts committed by male teenagers [1]. The probability density function of
the normal distribution is as Eq.(4.3) (see the function image in Fig. 4.4).
48 Trust Network Extraction in Large-Scale Trust-Oriented Social Networks
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
2
2.5
3
3.5
4
y
x
0 0.04
normal distribution
δ
x1 x1+δ
Figure 4.4: Normal distribution
y =1√
2πσ2e−
(x−µ)2
2σ2 (4.3)
where parameters µ and σ are the mean and standard deviation respectively, controlling
the curve of the function image.
In our model, we assume the probability distribution of a social interaction be-
tween any two participants with the social contextual impact factors also follows the
normal distribution. Let P (A → B|X) denote the probability of A and B have so-
cial interactions, where X is the value of each item included in Eq (4.1) (i.e., PSDiAB,
RLDAB) and |CIFDiA − CIFDi
B |).Then, based on mathematical theory of the integration [11], P (A → B|X) can be
calculated by Eq. (4.4). In this equation, δ is the length of each small interval (the
horizontal axis between 0 and 1 is divided into several small intervals [11]). If X is
in one of the intervals (e.g., in the interval [x1, x1 + δ] in Fig. 4.4), P (A → B|X)
is the integration of Eq. (4.3) with a lower limit X and an upper limit X + δ (in the
case shown in Fig. 4.4, where X = x1). Namely, P (A → B|X) is equal to the
corresponding area of the trapezoid with curved edges in an interval [X,X + δ] (e.g.,
the shadowed area in Fig. 4.4). In addition, the parameters µ and σ in Eq. (4.4) can be
computed by applying social statistics methods and mathematical theories in a social
network [11, 12]. But this problem is out of the scope of this thesis. Finally, based on
probability theory [11], the aggregated social interaction probability between A and B
§4.3 The Proposed SCAN Algorithm for Trust Network Extraction 49
(denoted as AP (A → B)) can be calculated by Eq. (4.5).
P (A → B|X) =
∫ X+δ
X
1√2πσ2
e−(X−µ)2
2σ2 d(X) (4.4)
AP (A → B) =∏
P (A → B|X) (4.5)
In our model, the aggregated social interaction probability will be considered in the
node selection of trust network discovery, where the larger the probability of a node to
have a social interaction with the target, the more likely for the node to be selected.
To solve the NP-Complete trust network discovery problem with QoTN constraints,
we propose a Social Context-Aware trust Network discovery (SCAN) algorithm, by
adopting the Monte Carlo method and two optimization strategies.
4.3.1 Monte Carlo Method
Monte Carlo method Monte Carlo method [43] is a computational algorithm that re-
lies on repeated random sampling to solve a problem. The specific areas of application
of the Monte Carlo method include computational physics, physical chemistry, global
illumination computations, finance and business, and computational mathematics (e.g.
numerical integration and numerical optimization) [43, 104]. It is also one of the tech-
niques with good efficiency for solving NP-complete problems [43, 104]. In the liter-
ature, based on the Monte Carlo method, a number of algorithms have been proposed
for solving NP-Complete problems [43, 73, 104].
4.3.2 Algorithm Description of SCAN
Based on the Monte Carlo method, we propose an approximation algorithm for So-
cial Context-Aware trust Network (SCAN) selection problem. In SCAN, initially, the
source participant vs is regarded as the current expansion node (the node as the start
point of the next step search), and SCAN searches all the neighboring nodes of vs
50 Trust Network Extraction in Large-Scale Trust-Oriented Social Networks
(denoted as vs.neighboring node) to investigate whether the current node and its cor-
responding links satisfy the QoTN constraints. If all QoTN constraints can be satisfied,
the neighboring node is called a feasible node (denoted as vf ). Given that the larger
the outdegree of a node, the more likely the node is to have a connection with oth-
ers [2], SCAN calculates the selection probability of all the feasible nodes (denoted as
SCP (vf → vt)) based on AP (vf → vt) and the outdegree of vf (denoted as deg+(vf ))
by Eq. (4.6).
SCP (vf → vt) = AP (vf → vt) · deg+(vf )
MAX(deg+)(4.6)
where MAX(deg+) is the maximal value of the outdegree of the nodes in a social
network.
After that, based on their selection probabilities, SCAN selects one of the feasible
nodes as the next expansion node (denoted as vexp), where the higher the selection
probability of a node, the more likely for the node to be selected. During the process,
a cycle in a path is avoided by the strategy in [109], as it leads to inefficiency and
ineffectiveness of the network discovery [91]. Finally, SCAN repeats the above search
process at each vexp until it finds vt or reaches the threshold of search hops (denoted
as λh, on average λh ≤ 7 due to the small-world phenomenon of social networks.
During the search process, in addition to the basic Monte Carlo method, we adopt the
following two optimization strategies to improve the efficiency of our algorithm.
Optimization Strategy 1: Avoiding Repeated Feasibility Investigations in Sim-
ulations. In each search step, the Monte Carlo method investigates the feasibility of all
the neighboring nodes of the current vexp (e.g., investigating vx, vy and vz in Fig. 4.5).
In multiple simulations of the Monte Carlo method, a node may be selected as a vexp
more than once. In such a situation, the feasibility investigation needs to be performed
repeatedly, leading to low efficiency. To address this issue, in SCAN, if a neighbor-
ing node is infeasible, (e.g., vx in Fig. 4.5), the corresponding link from the current
vexp to the neighboring node (e.g., vm → vx) will be removed. Then, upon reaching
§4.3 The Proposed SCAN Algorithm for Trust Network Extraction 51
the same vexp (e.g., vm) in the subsequent simulations, SCAN does not investigate its
neighboring nodes repeatedly as all of them are feasible.
Figure 4.5: Unsatisfied nodes
Optimization Strategy 2: Avoiding Repeated Probability Calculations in Sim-
ulations. In multiple simulations of the Monte Carlo method, if the same vexp is
selected more than once (e.g., vm in Fig. 4.5 is selected more than once), its feasible
neighboring nodes’ selection probabilities will have to be calculated repeatedly, lead-
ing to low efficiency. To address this issue, at each feasible node, SCAN records its
selection probability (denoted as v.selection), thereby avoiding repeated calculations
in the subsequent simulations.
Given a group of QoTN constraints, and a pair of vs and vt in a complex contextual
social network, the process of SCAN includes the following steps.
4.3.3 The Process of SCAN
Initialization: At each node vi, set vi.probability status = 0, which indicates the so-
cial interaction probabilities of vi’s neighboring nodes (denoted as vi.neighboring nodes)
have not been calculated. In addition, all the nodes are marked as unvisited (vi.visit =
0), and set vexp = vs.
Step 1: Based on vexp.probability status, SCAN performs the following search
strategies.
If vexp.probability status 6= 1, SCAN investigates the feasibility of vj , vj ∈
52 Trust Network Extraction in Large-Scale Trust-Oriented Social Networks
{vexp.neighboring nodes}) as follows.
(a) Case 1: If vj = vt, then SCAN terminates the current search, and starts a
new simulation from Initialization.
(b) Case 2: If vj 6= vt and vj is a feasible node, then SCAN calculates
SCP (vj → vt), and sets vj.selection = SCP (vj → vt) and
newline vexp.probability status = 1.
(c) Case 3: If vj 6= vt and vj is an infeasible node, based on the number of the
infeasible neighboring nodes of vexp (denoted as vexp.infeasible number),
SCAN performs the following search strategies.
(c-1-1): If vexp.infeasible number = vexp.neighboring nodes and
vexp = vs, then SCAN terminates, failing to return a trust network that
satisfies QoTN constraints.
(c-1-2): If vexp.infeasible number = vexp.neighboring nodes and
vexp 6= vs, then SCAN terminates the current search and starts a new
simulation from initialization.
(c-1-3): If vexp.infeasible number 6= vexp.neighboring nodes, go
to Step 2.
Step 2. If vsel.visit = 0, calculate the probability of vj to be a vexp by the following
Eq.(4.7).
p(vj) =vj.selection∑vk.selection
vk ∈ {vexp.neighboring node} (4.7)
Step 3. Select one of the feasible neighboring nodes (denoted as vsel) based on
their probabilities obtained by Eq. (4.7). Then based on Optimization Strategy 1, set
vsel.visit = 1, to avoid cycles in the subsequent search steps of the current simulation.
Step 4. Set vexp = vsel, and continue the search from Step 1 until the number of
searching hops reaches λh (on average λh ≤ 7[101]).
The time complexity of SCAN is O(sld), where s is the number of simulations; l
is the average length of the social trust paths from vs to vt; d is the maximal outdegree
§4.4 Experiments on SCAN 53
0 1000 2000 3000 4000 50000
50
100
simulation times (QoTN constraint ID #1)
utili
ty
0 1000 2000 3000 4000 50000
20
40
60
simulation times (QoTN constraint ID #2)
utili
ty
0 1000 2000 3000 4000 50000
20
40
simulation times (QoTN constraint ID #3)
utili
ty
0 1000 2000 3000 4000 50000
20
40
simulation times (QoTN constraint ID #4)
utili
ty
RWS
RWS RWS
HDS HDS
HDS HDS
SCANSCAN
SCANSCAN
RWS
Figure 4.6: The utilities of extracted trust networks with 4 hops
0 1000 2000 3000 4000 50000
50
100
150
simulation times (QoTN constraint ID #1)
utili
ty
0 1000 2000 3000 4000 50000
20
40
60
80
simulation times (QoTN constraint ID #2)
utili
ty
0 1000 2000 3000 4000 50000
20
40
60
80
simulation times (QoTN constraint ID #3)
utili
ty
0 1000 2000 3000 4000 50000
20
40
simulation times (QoTN constraint ID #4)
utili
ty
RWS
HDS HDS
HDS
RWS
RWSRWS
SCANSCAN
SCANSCAN
HDS
Figure 4.7: The utilities of extracted trust networks with 6 hops
of the nodes in social networks. In social networks, on average, l < 7 [101]. Thus
the time complexity of SCAN is O(sd), which is better than FBS (Flooding Based
Search) with the time complexity of O(dTTL) (TTL is Time To Live, introduced in
Section 2.3), and the same as those of both RWS (Random Walk Search) and HDS
(High Degree Search).
54 Trust Network Extraction in Large-Scale Trust-Oriented Social Networks
0 1000 2000 3000 4000 50000
500
1000
1500
simulation times (QoTN constraint ID #1)
exec
utio
n tim
e (s
ec)
0 1000 2000 3000 4000 50000
1000
2000
simulation times (QoTN constraint ID #2)
exec
utio
n tim
e (s
ec)
0 1000 2000 3000 4000 50000
1000
2000
simulation times (QoTN constraint ID #3)
exec
utio
n tim
e (s
ec)
0 1000 2000 3000 4000 50000
1000
2000
simulation times (QoTN constraint ID #4)
exec
utio
n tim
e (s
ec)
RWS RWS
RWS RWS
HDS HDS
HDS HDS
SCAN SCAN
SCAN SCAN
Figure 4.8: The execution time (4 hops)
0 1000 2000 3000 4000 50000
500
1000
1500
simulation times (QoTN constraint ID #1)
exec
utio
n tim
e (s
ec)
0 1000 2000 3000 4000 50000
500
1000
1500
simulation times (QoTN constraint ID #2)
exec
utio
n tim
e (s
ec)
0 1000 2000 3000 4000 50000
1000
2000
simulation times (QoTN constraint ID #3)
exec
utio
n tim
e (s
ec)
0 1000 2000 3000 4000 50000
1000
2000
simulation times (QoTN constraint ID #4)
exec
utio
n tim
e (s
ec)
RWS RWS
RWS RWS
HDS HDS
HDS
HDS
SCAN SCAN
SCAN SCAN
Figure 4.9: The execution time (6 hops)
4.4 Experiments on SCAN
4.4.1 Experimental Setup
Firstly, in order to evaluate the performance of our proposed algorithm SCAN on trust
network discovery, we need a dataset that contains social network structures. The
Enron email dataset (https://www.cs.cmu.edu/ enron/) has been proved to possess the
small-world and power-law characteristics of social networks and thus it has been
widely used in the studies of social networks [79, 82, 96, 117]. To validate our pro-
§4.4 Experiments on SCAN 55
posed algorithm, we select the Enron email dataset with 87,474 nodes (participants)
and 30,0511 links (formed by sending and receiving emails) as the dataset for our ex-
periments. Secondly, we randomly select a source and a target from the dataset, and
compare our SCAN with other methods in all the three categories, i.e., FBS, RWS and
HDS (see Chapter 2.2.3). Thirdly, we set four groups of QoTN constraints as listed in
Table 4.1 and set the social interaction probability to approximately follow the normal
distribution with µ = 0.5 and σ = 0.1. Finally, since the detailed mining method of
social contextual impact factor values is out of the scope of this thesis, their values are
generated by using the function normrnd(µ, σ) in Matlab, which generates random
numbers in the range of [0, 1], following the normal distribution with µ and σ.
Each of SCAN, FBS, RWS and HDS is implemented using Matlab R2008a running
on an Lenovo ThinkPad SL500 laptop with an Intel Core 2 Duo T5870 2.00GHz CPU,
3GB RAM, Windows XP SP3 operating system and MySql 5.1.35 relational database.
The results are plotted in Fig. 4.6 to Fig. 4.9, where the execution time and the
utilities of the extracted trust network for each of the algorithms are averaged based on
10 independent runs. In each run, we perform up to 5000 simulations.
Table 4.1: The settings of QoTN constraintsID QoTN(T ) QoTN(SI) QoTN(PS) QoTN(RLD) QoTN(ρ)1 0.10 0.10 0.10 0.10 0.102 0.15 0.15 0.15 0.15 0.153 0.20 0.20 0.20 0.20 0.204 0.25 0.25 0.25 0.25 0.25
4.4.2 Results and Analysis
During the execution of FBS with TTL=2, MATLAB runs out of memory. This could
be caused by the large outdegrees of the nodes in the two search hops. Therefore, we
compare the extracted trust networks’ utilities delivered by SCAN, RWS and HDS and
their execution time.
Fig. 4.6 to Fig. 4.7 plot the extracted trust networks’ utilities with different QoTN
56 Trust Network Extraction in Large-Scale Trust-Oriented Social Networks
Table 4.2: The comparison of the utility
SimulationsDifference of path utility
4 hops 5 hops 6 hops 7 hops total1000 19.24%more 45.02%more 112.37%more 114.15%more 72.69%more2000 62.40%more 61.68%more 63.29%more 118.71%more 76.52%more3000 103.84%more 88.18%more 41.08%more 104.62%more 84.43%more4000 114.80%more 101.68%more 40.13%more 84.42%more 85.25%more5000 139.55%more 92.51%more 37.55%more 64.78%more 71.12%more
Table 4.3: The comparison of execution time (5000 simulations)
AlgorithmsThe sum of the average execution time (sec)
4 hops 5 hops 6 hops 7 hops totalSCAN 532.5590 772.2890 910.7940 1.1280e+003 3.3436e+003RWS 6.0538e+003 5.8048e+003 5.9819e+003 6.3017e+003 2.4142e+004HDS 1.6466e+003 2.0008e+003 2.3238e+003 2.5434e+003 8.5146e+003
SCAN/RWS 0.0880 0.1330 0.1523 0.1790 0.1385SCAN/HDS 0.3234 0.3836 0.3919 0.4435 0.3927
constraints with 4 and 6 search hops (the figures for 5 and 7 hops are similar to those
of 4 and 6). From them we could see that firstly, with the same simulation times, our
proposed SCAN can deliver much higher network utilities than all the other methods
in all cases. In addition, since HDS cannot find vt after 5000 times search from vs in all
cases, the extracted trust network’s utility delivered by HDS is always zero. Thus, we
compare the average utilities based on different QoTN constraints delivered by SCAN
and RWS in Table 4.2. From them we could see that, on average, SCAN can deliver
extra 72.69%, 76.52%, 84.43%, 85.25% and 71.12% more utilities respectively than
RWS with 1000, 2000, 3000, 4000 and 5000 simulations. This is because SCAN takes
into account the influence of social context on social interactions, where the larger the
probability that a node has a social interaction with vt, the more likely for the node to
be selected. This method increases the probability of finding a trust path from vs to vt
at each search run. In addition, SCAN considers the QoTN constrains, and can avoid
searching infeasible nodes, improving the effectiveness of each search.
Fig. 4.8 to Fig. 4.9 plot the execution time of SCAN, RWS and HDS with different
QoTN constraints with 4 and 6 search hops (the figures for 5 and 7 hops are similar
§4.5 The Proposed H-SCAN for Trust Network Extraction 57
to those of 4 and 6). From the results, we could see that the execution time of SCAN
is less than that of RWS in all cases. In addition, when the simulation times are less
than 1000, the execution time of SCAN is similar to HDS. But with the increase of
simulation times, HDS consumes much more execution time than SCAN. The average
execution time of HDS, RWS and SCAN in each of 4 to 7 search hops is listed in
Table 4.3. Based on the statistics of all executions, on average, the execution time of
SCAN is only 13.85% and 39.27% of those of RWS and HDS respectively. This is
because SCAN avoids repeated feasibility investigation (by Optimization Strategy 1)
and repeated selection probability calculation (by Optimization Strategy 2).
Summary: Based on the above experimental results and analysis, we conclude
that our proposed SCAN outperforms all the existing methods significantly in both
execution time and the quality of the extracted trust networks. Therefore, SCAN is an
efficient and effective algorithm for the trust network discovery with QoTN constrains
in complex contextual social networks.
4.5 The Proposed H-SCAN for Trust Network Extrac-
tion
4.5.1 K-Best-First Search (KBFS)
K-Best-First Search (KBFS) algorithm [34] is based on the Best-First Search method,
which expands up to the best K nodes in the OpenSet (i.e., a set to store all candidates)
in each cycle of node expansion. KBFS is one of the best heuristic algorithms with
good efficiency for solving NP-complete problems, such as the Number Partitioning
problem and n-Puzzle problem [6, 34]. The K best nodes selection method can also
be used in node selection in trust network extraction. However, KBFS is not directly
designed for the trust network extraction problem. During search, for example, KBFS
may (1) access a node with deg+ = 0, and (2) repeatedly investigate the feasibility of
an expansion node’s neighboring nodes.
58 Trust Network Extraction in Large-Scale Trust-Oriented Social Networks
4.5.2 Algorithm Description of H-SCAN
Based on KBFS, we propose a Heuristic algorithm for Social Context-Aware trust
Network (H-SCAN) selection problem. In H-SCAN, initially, the source participant vs
is regarded as the current expansion node, and H-SCAN searches all the neighboring
nodes of vs (denoted as vs.neighbors) to investigate whether the current node and
its corresponding links satisfy the QoTN constraints. If all QoTN constraints can be
satisfied, the neighboring node is called a feasible node (denoted as vf ). Because the
larger the outdegree of a node, the more likely for the node to have a connection with
others [2], H-SCAN calculates the selection probability of each the feasible nodes vf
(i.e., SCP (vf → vt) in Eq. 4.6).
After that, H-SCAN selects up to K feasible neighboring nodes which have the
K maximum selection probabilities, as the next expansion nodes (i.e., vexp). Finally,
H-SCAN repeats the above search process at each vexp until it reaches the threshold
of search hops (i.e., λh, on average λh ≤ 7 due to the small-world phenomenon of
social networks. During the search process, we adopt the following three optimization
strategies to improve the efficiency of H-SCAN.
Optimization Strategy 1: Avoid Investigating the Intermediate Nodes with
deg− > 0 and deg+ = 0. According to the power-law characteristic of social net-
works, most of the nodes in a social network have a small outdegree [103]. Therefore,
there can be many nodes with deg− > 0 and deg+ = 0. During KBFS search, a node
(denoted as vx, vx 6= vt) with deg+(vx) = 0 and deg−(vx) > 0 (e.g., vx in Fig. 4.10)
may be investigated as a candidate of expansion nodes. As there is no social trust path
linking vx and vt, the investigation of such a node may lead to low efficiency. To avoid
this problem, H-SCAN does not investigate the feasibility of vx and does not select
such a node as an expansion node in the subsequent search. This strategy improves the
efficiency and effectiveness of the trust network discovery.
Optimization Strategy 2: Avoid Repeatedly Accessing the Neighboring Nodes
of An Expansion Node. During KBFS search, an expansion node vexp may be se-
§4.5 The Proposed H-SCAN for Trust Network Extraction 59
Vm
Vx
deg+=0, deg-=1
Vs ! ! Vt
! !
! !
an expansion node
Figure 4.10: A case of accessing the node with deg+ = 0
lected more than once in different search hops (e.g., vexp = vc in Fig. 4.11). In such
a situation, the feasibility of vexp’s neighboring nodes will be repeatedly investigated
(e.g., vd in Fig. 4.11), leading to low efficiency. To address this issue, upon reach-
ing the same vexp (e.g., vb) in different search hops, H-SCAN does not investigate its
neighboring nodes repeatedly as all of them have been visited in previous search, thus
saving execution time.
Vm
Vb
Vs ! ! Vc ! !
the current
expansion node
previous
expansion node
Figure 4.11: Repeated selecting the same expansion node in different search steps
4.5.3 The Process of H-SCAN
Given a group of QoTN constraints, and a pair of vs and vt in a complex contextual
social network, the process of H-SCAN includes the following steps. The pseudo-code
of H-SCAN is given in Algorithm 4.5.
Initialization: At each node vk, set vk.expansion = 0, which indicates vk’s neigh-
boring nodes has not been selected as an expansion node. In addition, set two sets to
record up to K current expansion nodes (i.e., ClosedSet [116]) and all the candidates
for the search of the next hop (i.e., OpenSet [116]), respectively. Furthermore, put vs
60 Trust Network Extraction in Large-Scale Trust-Oriented Social Networks
Algorithm 1: H-SCANData: MT (vs, vt), vs, vt, QoTNη
vs,vt , K, λh
Result: TN(vs, vt)1 begin2 Set vk.expansion = 0, vk.preNumber = 0, hops = 1, ClosedSet = vs, OpenSet = ∅;3 while hops ≤ λh do4 for each vi ∈ ClosedSet do5 vi.expansion = 1;6 for each vj ∈ adj[vx] do7 if QoTNη
vi,vjcan be satisfied and vj .expansion = 1 then
8 vj .preNumber = vj .preNumber + 1;9 m = vj .preNumber;
10 vj .preNode(m) = vi;end
11 if QoTNηvi,vj
can be satisfied and vj .expansion = 0 then12 if vj = vt then13 vj .preNumber = vj .preNumber + 1;14 m = vj .preNumber;15 vj .preNode(m) = vi;
end16 else if deg+(vj) > 0 and vj 6= vt then17 vj .preNumber = vj .preNumber + 1;18 m = vj .preNumber;19 vj .preNode(m) = vi;20 Put vj into OpenSet;
endend
endend
21 ClosedSet = up to the K Maximal SCP (vj → vt) , vj ∈ OpenSet;22 hops = hops + 1;
end23 if vt.preNumber > 0 then24 Put vt into preset;25 while preSet 6= ∅ do26 for each vm ∈ preSet do27 Delete vm from preSet;28 for i = 1 to vm.preNumber do29 Add vm, vm.preNode(i) and vm.preNode(i) → vm into TN(vs, vt);30 if vm.preNode(i) 6= vs then31 Put vm.preNode(i) into preSet;
endend
endend
endend
into ClosedSet and set the number of current search hop as one (denoted as hops = 1)
(lines 1-2 in Algorithm 1).
Step 1: If there exists any vi.expansion = 0, (vi ∈ ClosedSet) and hops ≤ λh,
get vi from ClosedSet, and mark vi.expansion = 1. Otherwise, go to Step 3 (lines
3-5 in Algorithm 1).
Step 2: Investigates vj , (vj ∈ vi.neighbors). If vj is a feasible node, based on the
§4.5 The Proposed H-SCAN for Trust Network Extraction 61
value of vj.expansion, H-SCAN performs the following search strategies.
Situation 1: If vj.expansion = 1 and the corresponding QoTN constraints can
be satisfied, then the number of the preceding nodes of vj increases by 1 (denoted
as vj.preNumber = vj.preNumber +1). In addition, let m = vj.preNumber.
At vj , store the mth preceding node of vj (denoted as vj.preNode(m) = vi)
(lines 6-10 in Algorithm 1).
Situation 2: If vj.expansion = 0 and the corresponding QoTN constraints can
be satisfied, based on the status of vj , H-SCAN performs the following search
strategies.
Case 1: If vj = vt, then the number of the preceding nodes of vj in-
creases by 1 (i.e., vj.preNumber = vj.preNumber + 1). In addition, let
m = vj.preNumber, at vj , store the mth preceding node of vj (denoted as
vj.preNode(m) = vi) (lines 11-15 in Algorithm 1) .
Case 2: If vj 6= vt and deg+(vj) > 0, then the number of the preceding
nodes of vj is increased 1 (i.e., vj.preNumber = vj.preNumber + 1). In
addition, let m = vj.preNumber, at vj , store the mth preceding node of
vj (i.e., vj.preNode(m) = vi). Finally, put vj into OpenSet (lines 16-20
in Algorithm 1).
Step 3: Set hops = hops + 1. If hops <= λh and OpenSet 6= ∅, select up to
K candidate (denoted as vcand(K)) which have the K maximal SCP (vcand(K) → vt)
from OpenSet and put them into ClosedSet (lines 21-22 in Algorithm 1).
Step 4: If vt.preNumber > 0, construct the trust network from vs to vt (denoted
as TN(vs, vt)) by searching the preceding nodes from vt layer by layer until reaching
vs. Otherwise, it fails to return a trust network that satisfies QoTN constraints (lines
23-31 in Algorithm 1).
H-SCAN contains two parts, i.e., part 1: network search (Step 1 to Step 3) and
part 2: trust network construction (Step 4). At each search hop, H-SCAN selects up
62 Trust Network Extraction in Large-Scale Trust-Oriented Social Networks
to K expansion nodes; therefore, the time complexity of H-SCAN in network search
(i.e., the first part) is O(Kmλh), where K is the number expansion nodes selected at
each search hop; m is the maximal outdegree of the nodes in a social network, and
λh is the maximal search hops. In addition, in the worst case, there are K(λ − 1)
intermediate nodes and each intermediate node has K preceding nodes. Then the
time complexity of H-SCAN in trust network construction (i.e., the second part) is
O(K2λh). In social networks, on average, λh < 7 [101], and K ≤ m. Thus the
time complexity of H-SCAN is O(Km), which is better than TTL-BFS (Time To Live
based Breadth First Search) with the time complexity of O(mTTL), and the same as
both RWS (Random Walk Search) and HDS (High Degree Search). Since H-SCAN
considers the social contextual impact factors and adopts our proposed optimization
strategies, it can deliver higher utility and consume less execution time than TTL-BFS,
HDS and RWS.
4.6 The Proposed H-SCAN-K for Trust Network Ex-
traction
4.6.1 Drawbacks of H-SCAN
H-SCAN considers social contexts and the constraints specified by a source, and thus it
can greatly improve the effectiveness in trust network extraction. However, H-SCAN
still has some drawbacks that can lead to losing important nodes and links in trust
network extraction.
At each search step, if there are more than K neighboring nodes, H-SCAN selects
fixed K neighbors (e.g., v1 to vk in Case 1 and Case 2 in Fig. 4.12) with top K selection
probabilities. This strategy (1) may neglect some marginal nodes that also have high
likelihood to connect to the target (denoted as v+mg) (e.g., the selection probability of
vk is 0.81 and that of vk+1 is 0.8 in Case 1 in Fig. 4.12, then v+mg = vk+1), and (2) may
select some marginal nodes that have low likelihood to connect to the target (denoted
§4.6 The Proposed H-SCAN-K for Trust Network Extraction 63
as v−mg) (e.g., the selection probability of vk−1 is 0.8 and that of vk is 0.3 in Case 2 in
Fig. 4.12, then v−mg = vk).
… ...
.
.
.
… ...
Case 1 Case 2
Vm
V1
Vk
Vk+1
Vs
the selection probability of Vk is 0.81 and that of Vk+1 is 0.8
Vs Vm
.
.
.
V1
Vk-1
Vk
the selection probability of Vk -1 is 0.8 and that of Vk is 0.3
Figure 4.12: Drawbacks in H-SCAN
To address the above drawbacks included in KBFS and H-SCAN, we propose four
optimization strategies and two heuristic search strategies in the following subsections.
Then, based on these strategies, we propose a Heuristic Social Context-Aware trust
Network extraction algorithm (H-SCAN-K), where constraints and the social context
similarity between participants are considered.
4.6.2 Algorithm Description of H-SCAN-K
In H-SCAN-K, initially, the source participant vs is regarded as the current expansion
node, and H-SCAN-K searches all the neighboring nodes of vs (denoted as NE(vs))
to investigate whether the current node and its corresponding links satisfy the QoTN
constraints. If all QoTN constraints can be satisfied, the neighboring node is called a
feasible node (denoted as vf ). The larger the outdegree of a node, the more likely for
the node to have a social connection with others [2]. Thus, H-SCAN-K calculates the
selection probability of each of the feasible nodes vf in a specified domain (denoted
as SCPDivf ,vt
) based on SmiDivf ,vt
and the outdegree of vf (i.e., deg+(vf )) by Eq. (4.8).
64 Trust Network Extraction in Large-Scale Trust-Oriented Social Networks
SCPDivf ,vt
= SmiDivf ,vt
· deg+(vf )
MAX(deg+)(4.8)
where MAX(deg+) is the maximal outdegree of all nodes in a social network.
After that, based on SCPDivf ,vt
, in addition to the two optimization strategies pro-
posed in H-SCAN, H-SCAN-K selects the next expansion nodes (i.e., vexp) based on
two Optimization Strategies and two Heuristic Search Strategies discussed below. Fi-
nally, H-SCAN-K repeats the above search process at each vexp until it reaches the
threshold of search hops (i.e., λh, on average λh ≤ 7 conforming to the small-world
phenomenon). These strategies can improve the effectiveness and efficiency of trust
network extraction. This has been validated in our experiments (see experiments in
Section 4.7).
Optimization Strategy 1: Avoid Selecting Marginal Nodes v−mg. In H-SCAN, if
the number of the neighboring nodes of vexp is greater than K, the fixed K nodes with
top K selection probabilities will be selected as the expansion nodes for the subsequent
search (e.g., K = 3 in Fig. 4.13). However, as we discussed in Section 4.5, there may
be some marginal nodes (i.e., v−mg) among the selected K nodes (suppose the number
of margin nodes v−mg is n ∈ [1, K − 1]) whose selection probabilities are less than
that of the (K − n)th node (denoted as v(K−n)th) minus a small value (denoted as
gap). i.e., SCPDiv(K−n)th
,vt− SCPDi
v−mg ,vt> gap. That is, although these nodes have
been selected as part of the K expansion nodes, they have much lower likelihood to
connect to the target than other expansion nodes (e.g., v3 in Fig. 4.13). Extracting the
trust network via these nodes can lead to low effectiveness. To avoid this problem,
H-SCAN-K investigates K ′ (0 < K ′ < K) nodes. If there exist K ′′ (K ′′ ≤ K ′) v−mg
nodes in all the neighbors of an expansion node (e.g., K ′ = K ′′ = 1 in Fig. 4.13),
then only K − K ′′ nodes will be selected as the expansion nodes in the subsequent
search (e.g., only v1 and v2 are in the ClosedSet (a set stores all the expansion nodes)
of H-SCAN-K in Fig. 4.13).
Optimization Strategy 2: Avoid Neglecting Marginal Nodes v+mg. In H-SCAN,
§4.6 The Proposed H-SCAN-K for Trust Network Extraction 65
Vm
V1
V3
V4
Vs……
V2
K=3, K'=K''=1
SCPDi
v1,vt> SCPDi
v2,vt> SCPDi
v3,vt
SCPDi
v2,vt− SCPDi
v3,vt> gap
ClosedSet of H − SCAN : {v1, v2, v3}
ClosedSet of H − SCAN −K : {v1, v2}
Figure 4.13: v−mg nodes
there may be some marginal nodes (i.e., v+mg) whose selection probabilities are greater
than that of the Kth selected expansion node (denoted as vKth) minus gap (e.g., v8
in Fig. 4.14 is a marginal node v+mg). i.e. SCPDi
vK ,vt− SCPDi
v+mg ,vt
< gap. Although
these nodes are not included in the K selected expansion nodes, they still have a high
likelihood to connect to the target (e.g., v8 in Fig. 4.14). However, these nodes are
neglected by H-SCAN, leading to low effectiveness in trust network extraction. To
avoid this problem, in H-SCAN-K, suppose there are n∗ (n∗ > K) candidates in the
search of the current layer (e.g., n∗ = 4 in Fig. 4.14), in addition to the K best
nodes, H-SCAN-K investigates the selection probabilities of another K∗ nodes (K +
K∗ ≤ n∗). If there exist K∗∗ (K∗∗ ≤ K∗) v+mg nodes in the search of a layer (e.g.,
K∗ = K∗∗ = 1 in Fig. 4.14), then K + K∗∗ nodes will be selected as the expansion
nodes in the subsequent search of the next layer (e.g., all v5, v6, v7 and v8 are in the
ClosedSet of H-SCAN-K in Fig. 4.14).
In addition to the above optimization strategies, we propose two heuristic search
strategies and adopt them into a bidirectional search from vs and vt respectively to
extract the trust networks.
Heuristic Strategy 1 (Forward Search From vs To vt): The Forward Search pro-
cedure extracts the trust network by searching the nodes that have social connection
with vs and have high likelihood to connect to vt. In forward search, at each search
step, H-SCAN-K computes the social context similarity between each neighboring
66 Trust Network Extraction in Large-Scale Trust-Oriented Social Networks
Vm
V5
V7
V8
Vs……
V6
K=3, K*=K**=1
SCPDi
v6,vt> SCPDi
v7,vt> SCPDi
v8,vt
SCPDi
v7,vt− SCPDi
v8,vt< gap
ClosedSet of H − SCAN : {v5, v6, v7}
ClosedSet of H − SCAN −K : {v5, v6, v7, v8}
Figure 4.14: v+mg nodes
node and vt (no direct link with vt) based on Eq. (4.1), and calculates the correspond-
ing selection probability based on Eq. (4.8). Then H-SCAN-K selects up to K + K∗∗
(or K − K′′) expansion nodes based on Optimization Strategies 1 to 4. During this
process, if a neighboring node has been selected by the following Heuristic Strategy 2
(i.e., the node has social connection with vt), the node will be regarded as an expan-
sion node for subsequent search and the link from the current expansion node to the
selected neighboring node is added into the extracted trust network. H-SCAN-K will
then continue the above search process until the number of search hops reaches six.
Heuristic Strategy 2 (Backward Search From vt To vs): The Backward Search
procedure extracts the trust network by searching the nodes which have social con-
nections with vt and have a high likelihood to connect to vs. At each search step,
H-SCAN-K computes the social context similarity between vs and those nodes that
have social connections with vt based on Eq. (4.1), and calculates the corresponding
selection probability based on Eq. (4.8). Then H-SCAN-K selects up to K + K∗∗
(or K − K′′) expansion nodes based on the Optimization Strategies 1 to 4. During
this process, if a neighboring node has been selected by the above Heuristic Strategy
1 (i.e., the node has social connection with vs), the node will be regarded as an expan-
sion node for subsequent search and the link from the pre-visited neighboring node to
the current expansion node will be added into the extracted trust network. H-SCAN-K
will then continue the above search until the number of the search hops reaches six.
§4.6 The Proposed H-SCAN-K for Trust Network Extraction 67
Vs … ... Vm Vt… ...
Forward-Search Backward-Search
Figure 4.15: The property of bidirectional search
Our bidirectional search strategy is based on the social context similarity between
an intermediate node and vt, and the node and vs (e.g., vm in Fig. 4.15), which tends
to link those intermediate nodes which connect to both vs and vt (e.g., vm), which can
improve the efficiency and effectiveness of trust network extraction (see experiments
in Section 4.7)
4.6.3 The Process of H-SCAN-K
Given a group of QoTN constraints, and a pair of vs and vt in a large-scale and com-
plex contextual trust-oriented social network, the process of H-SCAN-K includes the
following steps. The pseudo-code of H-SCAN-K is given in Algorithm 2 to Algorithm
4 (the notations used in the algorithm are explained in the Appendix).
Algorithm 2: H-SCAN-KData: vs, vt, QoTNη
vs,vt , K, K∗, K′, gapResult: TN(vs, vt)
1 begin2 v.fvisit = 0, v.bvisit = 0, hops = 0 λh = 6;3 f − ClosedSet = vs, b− ClosedSet = vt;4 while hos <= λh do5 Forward-Search;6 Backward-Search;7 hops = hops + 1;
end8 establish the trust network based on f − TN and b− TN ;
end
Initialization: At each node vk, set vk.fvisit = 0 and vk.bvisit = 0, which
indicates that vk has not been selected as an expansion node in Forward Search and
Backward Search respectively. In addition, set two sets to record the current expansion
68 Trust Network Extraction in Large-Scale Trust-Oriented Social Networks
Algorithm 3: Forward-Search1 begin
Set f −OpenSet = ∅;2 for each vi ∈ f − ClosedSet do3 for each vj ∈ NE(vi) do4 if QoTNη
vi,vjcan be satisfied then
5 if vj .fvisit == 1 || vj == vt then6 add vj and vi → vj into f − TN ;
end7 else if vj .bvisit = 1 then8 add vj and vi → vj into f − TN ;9 put vj into f − ClosedSet;
10 vj .fvisit = 1;11 else if vj .bvisit = 0 then12 add vj and vi → vj into f − TN ;13 put vj into f −OpenSet;14 vj .fvisit = 1;
endend
endend
end15 if f − ClosedSet 6= ∅ then16 select K + K∗∗ (or K −K′′) expansion nodes from f − ClosedSet;
end17 else18 stop Forward-Search;
end19 return f − TN ;
end
nodes in forward search and backward search respectively (i.e., f − ClosedSet and
b− ClosedSet) to record all the candidates of expansion nodes for subsequent search
(i.e., f − OpenSet and b − OpenSet). Furthermore, set the maximal search hop λh
as 6, put vs into f −ClosedSet and vt into b−ClosedSet, then set the number of the
current search hop as one (lines 1-3 in Algorithm 2).
Step 1 (Forward-Search): If there exists any vi.fivisit = 0 (vi ∈ f−ClosedSet),
get vi from f − ClosedSet; otherwise, terminate Forward-Search and return the ex-
tracted trust network (denoted as f − TN ) (lines 1-2 in Algorithm 3).
Step 2: Investigate vj , (vj ∈ NE(vi)). If vj is a feasible node, based on the status
of vj , H-SCAN-K performs the following search strategies (lines 3-5 in Algorithm 3)
Situation 1: If vj.fvisit = 1 or vj = vt, add vj and vi → vj , into f −TN (lines
6-7 in Algorithm 3).
Situation 2: If vj.fvisit = 0 and vj.bvisit = 1, add vj and vi → vj , into
§4.6 The Proposed H-SCAN-K for Trust Network Extraction 69
Algorithm 4: Backward-Search1 begin
Set b−OpenSet = ∅;2 for each vb ∈ b− ClosedSet do3 for each va ∈ PreNE(vb) do4 if QoTNη
va,vbcan be satisfied then
5 if va.bvisit == 1 || va == vs then6 add va and va → vb into b− TN ;
end7 else if va.fvisit = 1 then8 add va and va → vb into b− TN ;9 put va into b− ClosedSet;
10 va.bvisit = 1;11 else if va.fvisit = 0 then12 add va and va → vb into b− TN ;13 put va into b−OpenSet;14 va.bvisit = 1;
endend
endend
end15 if b− ClosedSet 6= ∅ then16 Select K + K∗∗ (or K −K′′) expansion nodes from b− ClosedSet;
end17 else18 Stop Backward-Search;
end19 return b− TN ;
end
f − TN , and put vj into f −ClostedSet. Then set vj.fvisit = 1 (lines 8-10 in
Algorithm 3).
Situation 3: If vj.fvisit = 0 and vj.bvisit = 0, add vj and vi → vj , into
f − TN , and put vj into f − OpenSet. Then set vj.fvisit = 1 (lines 11-14 in
Algorithm 3).
Step 3 : Select K + K∗∗ (or K − K ′′) expansion nodes from f − OpenSet; put
them into f − ClosedSet respectively; and return f − TN . (lines 15-19 in Algorithm
4).
Step 4 (Backward-Search): If there exists any vb.bvisit = 0 (va ∈ b−ClosedSet),
get vb from b− ClosedSet; otherwise, terminate Backward-Search and return the ex-
tracted trust network (denoted as b− TN ) (lines 1-2 in Algorithm 4).
Step 5: Investigate va, which has direct link to vb (i.e., va → vb, denoted as va ∈PreNE(vb)). If va is a feasible node, based on the status of va, H-SCAN-K performs
70 Trust Network Extraction in Large-Scale Trust-Oriented Social Networks
the following search strategies (lines 3-5 in Algorithm 4).
Situation 1: If va.bvisit = 1 or va = vs, add va and va → vb, into b−TN (lines
6-7 in Algorithm 4).
Situation 2: If va.fvisit = 0 and va.fvisit = 1, add va and va → vb, into
b− TN , and put va into f − ClostedSet. Then set va.bvisit = 1 (lines 8-10 in
Algorithm 4).
Situation 3: If va.fvisit = 0 and va.bvisit = 0, add va and va → va, into
b − TN , and put va into b − OpenSet. Then set va.bvisit = 1 (lines 11-14 in
Algorithm 4).
Step 6 : Select K + K∗∗ (or K − K ′′) expansion nodes from b − OpenSet; put
them into b− ClosedSet respectively; return b− TN . (lines 15-19 in Algorithm 4).
Step 7: Set hops = hops + 1. If both Forward-Search andBackward-Search ter-
minate, H-SCAN-K establish the trust network based on f − TN and b − TN by
searching the preceding nodes from vt and succeeded nodes from vs layer by layer
respectively. (lines 7-8 in Algorithm 2).
H-SCAN-K performs a bidirectional search strategy, i.e., Forwards Search and
Backward Search. Each search procedure can be divided into two parts, i.e., trust
network search (Step 1 to Step 6) and trust network construction (Step 7). Let m =
MAX(deg+). In the worst case, at each search hop, H-SCAN-K selects up to K+K∗∗
expansion nodes; therefore, the time complexity of trust network search (i.e., the first
part) is O((K + K∗∗)mλh), where K is the number expansion nodes selected at each
search hop; K∗∗ is the number of v+mg; λh is the maximal search hops. In addition, in
the worst case, there are (K + K∗∗)(λ− 1) intermediate nodes and each intermediate
node has K + K∗∗ preceding nodes. Then the time complexity of H-SCAN-K in trust
network construction (i.e., the second part) is O((K +K∗∗)λh). In social networks, on
average, λh < 7 [101], and (K +K∗∗) ≤ m. Thus the time complexity of H-SCAN-K
is O(m2), which is better than TTL-BFS (Time To Live based Breadth First Search)
§4.7 Experiments on H-SCAN and H-SCAN-K 71
with the exponential time complexity of O(mTTL), and it is the same as RWS (Random
Walk Search), HDS (High Degree Search) and our previous H-SCAN. Since H-SCAN-
K adopts our proposed optimization strategies and novel heuristic search strategies
in a bidirectional search, it can deliver results with higher utility and consume less
execution time than each of TTL-BFS, HDS, RWS and H-SCAN. The experimental
results illustrate the significant performance difference.
4.7 Experiments on H-SCAN and H-SCAN-K
The objective of the experiments is to compare the performance difference between our
proposed H-SCAN-K and the existing methods on two real datasets of social networks.
4.7.1 Datasets
We select two real datasets of social networks to conduct experiments. They are En-
ron email dataset (cs.cmu.edu/enron/) and Epinions dataset (trustlet.org), whose social
network structures are formed based on different applications.
4.7.1.1 Enron Email Dataset
The social network based on the Enron email dataset is formed by sending and receiv-
ing emails, and it has been proved to possess the small-world and power-law charac-
teristics of social networks. This dataset has in fact been widely used in the studies of
social networks [79, 82, 96, 117]. Thus, we select the Enron email dataset with 87,474
nodes (participants) and 30,0511 links (formed by sending and receiving emails) for
our experiments.
4.7.1.2 Epinions Dataset
Epinions (epinions.com) is an online website that provides reviews of products, where
participants could specify the trust relations between each other based on the quality of
72 Trust Network Extraction in Large-Scale Trust-Oriented Social Networks
Table 4.4: The settings of QoTN constraintsID QoTN(T) QoTN(SI) QoTN(PS) QoTN(RLD) QoTN(CIF)1 0.2 0.2 0.1 0.1 0.12 0.1 0.1 0.2 0.2 0.13 0.1 0.1 0.1 0.2 0.2
Table 4.5: Algorithms compared in the experimentsAlgorithm ID Algorithm Name
1 Time To Live-Breadth First Search (TTL-BFS) [19]2 High Degree Search (HDS) [2]3 Random Walk Search (RWS) [45]4 H-SCAN [85]5 H-SCAN-K+HS16 H-SCAN-K+HS12
product reviews. The Epinions dataset contains a trust-oriented social network, where
the trust relations specified by a truster to a trustee form each link. The Epinions
dataset has also been proved to possess the properties of social networks [20], and
has been widely used in the studies of trust in online social networks [24, 87]. Thus,
we select the Epinions dataset available at TrustLet (trustlet.org) with 88,180 nodes
(participants) and 71,7667 links (formed by trust relations specified by participants)
for our experiments.
4.7.2 Experimental Setup
We randomly select 5 pairs of source nodes and target nodes from each of the two
social network datasets for extracting the trust network between them. In addition,
in order to have more detailed investigations on the performance of H-SCAN-K, we
introduce two versions of it. The first one, denoted as H-SCAN-K+HS1, adopts our
optimization strategies and Heuristic Search Strategy 1 only (i.e., the forward search
from vs). The second one, denoted as H-SCAN-K+HS2, adopts optimization strategies
and Heuristic Search Strategies 1 and 2 (bidirectional search). Then we compare their
performance with other methods including TTL-BFS, RWS, HDS and our proposed
§4.7 Experiments on H-SCAN and H-SCAN-K 73
H-SCAN. Table 4.5 lists these algorithms.
In addition, considering the small-world characteristic, we set the maximal search
hops of all the algorithms to 6. Moreover, we set three groups of QoTN constraints as
listed in Table 4.4. Finally, the impact factor values are generated by using the function
rand() in Matlab, which can simulate different cases in real social networks. As we
introduced in Chapter 2.3.2, these values can be mined by using data mining methods
but this is not within the scope of this thesis.
TTL-BFS, RWS, HDS, H-SCAN, H-SCAN-K+HS1 and H-SCAN-K+HS2 are im-
plemented using Matlab R2008a running on a desktop with an Intel Core i5 CPU
(2.80GHZ), 4GB RAM, Windows 7 Professional operating system and MySql 5.1.35
relational database. The results are plotted in Fig. 4.16 to Fig. 4.23, where the execu-
tion time for each of the algorithms and the utilities of the trust network extracted by
RWS (as its search is based on random walks) are averaged based on 3 independent
runs.
4.7.3 Results and Analysis
We use the ratio of utility to execution time (i.e., utility/execution time, termed as per-
formance ratio) to illustrate the efficiency and effectiveness of trust network extrac-
tion. The larger the ratio, the better the performance of an algorithm in trust network
extraction. Next, we analyse the experimental results in detail.
Result and Analysis #1: Fig. 4.16 and Fig. 4.17 plot the performance ratios of
TTL-BFS method on Enron email dataset and Epinions dataset respectively. From
these figures, we can see that only in a few cases (3 out of 25 cases in Enron email
dataset, and 2 out of 25 cases in Epinions dataset), TTL-BFS can extract the trust
networks (e.g., S1 in Fig. 4.16 and Fig. 4.17). In most of the cases (i.e., 90% of
all cases), TTL-BFS cannot extract any trust networks (e.g., S2 in Fig. 4.16 and Fig.
4.17). In addition, in all the cases in which trust networks can be extracted, only in one
of them (networkID=4 in Enron email dataset), TTL-BFS can extract the trust network
74 Trust Network Extraction in Large-Scale Trust-Oriented Social Networks
23
45
6
1
2
3
4
50
20
40
60
80
100
hops
Enron Email Dataset
networkID
utili
ty/e
xecu
tion
time
(sec
)S1: can extract the trust networks
S2: cannot extract the trust networks
Figure 4.16: The average performance ratio delivered by TTL-BFS on Enron email dataset
23
45
6
1
2
3
4
50
10
20
30
40
50
60
hops
Epinions Dataset
networkid
utili
ty/e
xecu
tion
time
(sec
)
S1: can extractthe trust networks
S2: cannot extract the trust networks
Figure 4.17: The average performance ratio delivered by TTL-BFS on Epinions dataset
§4.7 Experiments on H-SCAN and H-SCAN-K 75
by searching 4 hops from vs. In the rest of the cases in which trust networks can be
extracted, TTL-BFS can only extract the trust network by searching 2 to 3 hops from
vs. If the number of search hops is greater than 4, TTL-BFS cannot extract any trust
network in all cases (even when the execution time is greater than those of the other
algorithms).
This is because the time complexity of TTL-BFS is exponential in TTL (i.e.,
O(mTTL)). Namely, the execution time of TTL-BFS will increase exponentially with
the increase of the search hops (i.e., the TTL number). Therefore, it cannot extract the
social network when the maximal path length is more than 3. This can lead to losing
many important nodes and links in trust network extraction, and thus, TTL-BFS is in-
applicable to trust network extraction in large-scale trust-oriented social networks. So,
in the following experiments, we only compare the performance ratios of HDS, RWS,
H-SCAN H-SCAN-K+HS1 and H-SCAN-K+HS2, and their execution time.
Result and Analysis #2: Fig.4.18 and Fig. 4.19 plot the performance rations of
the above 5 algorithms on Enron email dataset and Epinions dataset respectively. From
these figures, we can see that in all cases of both datasets, the utilities of the solutions
delivered by HDS are always equal to zero (even when HDS has more execution time
than RWS, H-SCAN, H-SCAN-K+HS1 and H-SCAN-K+HS2). This is because HDS
searches nodes based the descending order of their outdegrees only, without consid-
ering the likelihood of any social connection between a node and the target. This can
lead to low effectiveness.
Result and Analysis #3: In addition to HDS, from Fig. 4.18 and Fig. 4.19, we
can see that both our proposed H-SCAN-K+HS1 and H-SCAN-K+HS2 have larger
performance ratios than HDS, RWS and H-SCAN. Table 4.6 lists their performance
ratios, where we can see that on average the performance ratio of H-SCAN-K+HS1
is 3.55 times more than that of H-SCAN, and 59.95 times more than that of RWS.
The performance ratio of H-SCAN-K+HS2 is 3.57 times more than that of H-SCAN
and 60.7 times more than that of RWS. Namely, with the same execution time, our
H-SCAN-K can extract the trust networks with much better utilities than RWS and
76 Trust Network Extraction in Large-Scale Trust-Oriented Social Networks
12
34
5
1
2
30
5
10
15
20
networkID
Enron Email Dataset
QoTNID
utili
ty/e
xecu
tion
time
(sec
)
HDSRWSH−SACNH−SCAN−K+H1H−SCAN−K+H2
S3: better
Figure 4.18: The comparison of average performance ratio on Enron email dataset
12
34
5
1
2
30
2
4
6
8
10
networkID
Epinions Dataset
QoTNID
utili
ty/e
xecu
tion
time
(sec
)
HDSRWSH−SCANH−SCAN−K+HS1H−SCAN−K+HS2
S3: better
Figure 4.19: The comparison of average performance ratio on Epinions dataset
§4.7 Experiments on H-SCAN and H-SCAN-K 77
1
2
3
4
1
2
3
4
50
1000
2000
3000
4000
k
Enron Email Dataset
networkID
utili
ty
H−SCAN−K+HS1H−SCAN−K+HS2
Figure 4.20: The average utilities delivered by H-SCAN-K+HS1 and H-SCAN-K+HS2 onEnron email dataset
H-SCAN.
This is because H-SCAN-K takes into account the influence of social contexts on
social interactions, where the larger the likelihood for a node to have social connec-
tions with vt and vs, the more likely for the node to be selected in search. This method
increases the probability of finding a good quality trust path from vs to vt. In addi-
tion, H-SCAN-K adopts the proposed optimization strategies, and thus it can (1) avoid
accessing nodes with deg+ = 0 and accessing the neighboring nodes of the same ex-
pansion node repeatedly (by Strategies 1 and 2 in H-SCAN), (2) neglect the marginal
nodes (i.e., v−mg) which have a low likelihood to connect to vt in all candidates (by
Strategy 1 in H-SCAN-K), and (3) consider those marginal nodes (i.e., v+mg) with a
high likelihood to connect to vt in all candidates (by Strategy 2 in H-SCAN-K).
To sum up, H-SCAN-K greatly outperforms RWS and H-SCAN in the efficiency
and the quality of the extracted trust networks. Next, we compare the performance of
H-SCAN-K+HS1 and H-SCAN-K+HS2.
Result and Analysis #4: Fig. 4.20 to Fig. 4.23 plot the average utility and the
average execution time for each of H-SCAN-K+HS1 and H-SCAN-K+HS2 with dif-
ferent K values in Enron email dataset and Epinions dataset. From these figures, we
78 Trust Network Extraction in Large-Scale Trust-Oriented Social Networks
1
2
3
4
1
2
3
4
50
5000
10000
15000
k
Epinions Dataset
networkID
utili
ty
H−SCAN−K+HS1H−SCAN−K+HS2
Figure 4.21: The average utilities delivered by H-SCAN-K+HS1 and H-SCAN-K+HS2 onEpinions dataset
can see that the utilities and the execution time of H-SCAN-K+HS2 in all cases are
always greater than those of H-SCAN-K+HS1. This is because in addition to the for-
ward search from vs in H-SCAN-K+HS1, H-SCAN-K+HS2 performs the backward
search from vt to search the nodes that have social connections with vt and high like-
lihood to connect to vs. This search can deliver better utilities but consumes more
execution time. Next, we compare their performance ratios.
From Fig. 4.18 and Fig. 4.19, we can see that in 19 out of 30 extracted trust
networks (6 from Enron email dataset, 13 from Epinions dataset), H-SCAN-K+HS2
can deliver much larger performance ratios than H-SCAN-K+HS1 (e.g. S3 in Fig. 4.18
and Fig. 4.19). From Table 4.6, we can see that on average the performance ratio of
H-SCAN-K+HS2 is 1.25% more than that of H-SCAN-K+HS1. That is, although H-
SCAN-K+HS2 consumes more execution time, it can extract trust networks with much
better utilities than H-SCAN-K+HS1, and thus H-SCAN-K+HS2 is more efficient and
effective than H-SCAN-K+HS1 in trust network extraction.
This is because in addition to the forward search, H-SCAN-K+HS2 considers the
nodes that have a social connection with vt and have a high likelihood to connect to vs
§4.7 Experiments on H-SCAN and H-SCAN-K 79
1
2
3
4
1
2
3
4
550
100
150
200
250
300
k
Enron Email Dataset
networkID
exec
utio
n tim
e (s
ec)
H−SCAN−K+HS1H−SCAN−K+HS2
Figure 4.22: The average execution time of H-SCAN-K+HS1 and H-SCAN-K+HS2 on Enronemail dataset
in backward search. This bidirectional search tends to search the intermediate nodes
that have a high likelihood to connect to both vs and vt. If these nodes can connect
to vs during the backward search, H-SCAN-K+HS2 can deliver better utilities than
H-SCAN-K+HS1. The experiments have shown that in most cases, H-SCAN-K+HS2
outperforms H-SCAN-K+H1S, and on average, it can extract more important nodes
and links with higher efficiency than H-SCAN-K+HS1 (i.e., 1.25% more performance
rations) in trust network extraction.
The two versions of H-SCAN-K have different characteristics. H-SCAN-K+HS1
will use less execution time but will extract a trust network with less utility than H-
SCAN-K+HS2. In contrast, H-SCAN-K+HS2 is to guarantee the utility of the ex-
tracted trust network but will consume more execution time than H-SCAN-K+HS1.
4.7.4 Summary
Based on the above experimental results and analysis, we conclude that TTL-BFS and
HDS are not suitable for trust network extraction in large-scale social networks due
to low effectiveness and efficiency of their search strategies. Although RWS and H-
80 Trust Network Extraction in Large-Scale Trust-Oriented Social Networks
1
2
3
4
1
2
3
4
50
500
1000
1500
k
Epinions Dataset
networkID
exec
utio
n tim
e (s
ec)
H−SCAN−K+HS1H−SCAN−K+HS2
Figure 4.23: The average execution time of H-SCAN-K+HS1 and H-SCAN-K+HS2 on Epin-ions dataset
SCAN can be used to extract trust networks, our proposed H-SCAN-K greatly outper-
forms them in the efficiency and the quality of the extracted trust networks. Therefore,
H-SCAN-K is an efficient and effective algorithm for trust network extraction with
QoTN constraints in large-scale trust-oriented social networks. H-SCAN-K can ex-
tract high quality trust networks which provide the basis to deliver a reasonable trust
evaluation result between two unknown participants.
§4.7 Experiments on H-SCAN and H-SCAN-K 81
Tabl
e4.
6:C
ompa
riso
nof
perf
orm
ance
ratio
Alg
orith
mID
The
aver
age
perf
orm
ance
ratio
Net
wor
kID
(Enr
onem
aild
atas
et)
Net
wor
kID
(Epi
nion
sda
tase
t)A
vera
ge1
23
45
67
89
10H
DS
00
00
00
00
00
0R
WS
0.27
790.
0342
0.65
390.
5792
0.11
310
0.03
750.
0196
0.00
230.
1067
0.18
24H
-SC
AN
2.41
113.
7528
3.63
948.
6094
3.75
071.
7544
1.94
641.
3436
1.37
762.
2297
3.08
15H
-SC
AN
-K+H
S114
.281
413
.456
712
.985
618
.526
113
.630
97.
1036
7.97
265.
9070
6.93
328.
5431
10.9
34H
-SC
AN
-K+H
S215
.672
314
.053
79.
7914
17.4
620
10.3
775
9.04
949.
1718
7.88
109.
0424
8.20
2411
.070
4
82 Trust Network Extraction in Large-Scale Trust-Oriented Social Networks
4.8 Conclusion
In this Chapter, we have proposed a general concept QoTN (Quality of Trust Network),
and a novel social context-aware trust network extraction model in large-scale trust-
oriented social networks. In addition, we have proposed a new Social Context-Aware
trust Network discovery algorithm (SCAN) by adopting the Monte Carlo method and
our proposed optimization strategies. Furthermore, we have proposed a new Heuristic
Social Context-Aware trust Network discovery algorithm, called H-SCAN, by adopt-
ing K-Best-First Search (KBFS) method and our proposed optimization strategies. Fi-
nally, we have proposed a new Heuristic Social Context-Aware trust Network extrac-
tion algorithm, called H-SCAN-K, by adopting K-Best-First Search (KBFS) method,
bidirectional search (i.e., search from both the source and the target nodes simultane-
ously) and our proposed novel heuristic strategies. The experimental results demon-
strate the superior performance of the proposed algorithms in both the quality of the
extracted trust networks and the execution time.
Our proposed highly efficient and effective trust network extraction methods pro-
vide a good foundation for performing trust inference methods to deliver reasonable
trust evaluation results, which can be used in the social network based recommenda-
tion systems to help find the most trustworthy recommenders.
Chapter 5
Finding the Optimal Social Trust Path
In Chapter 4 we have introduced the trust network extraction methods in large-scale
trust-oriented social networks. After extracting the trust network, we can evaluate
the trustworthiness of the target by using trust propagation methods to propagate the
trust via the social trust paths in the trust network. However, in large-scale trust-
oriented social networks, there could be tens of thousands of social trust paths between
a source participant and a target one [70]. Evaluating the trustworthiness of the target
participant based on all these social trust paths is very time consuming, and thus cannot
be applied into real applications [6]. Alternatively, we can search the optimal path
yielding the most trustworthy trust propagation result from multiple paths. We call
this the optimal social trust path selection problem that is known to be a challenging
research problem [78].
In the literature, Lin et al. [77] proposed an optimal social path selection method,
where all links are assigned the same weight and the shortest path between the source
participant and the target one is selected as the optimal one. This method neglects
trust information between participants. In another work [53], the path with the max-
imal propagated trust value is selected as the most trustworthy social trust path. In
addition, Wang et al. [125] proposed a social trust path selection method where a
source participant can specify a threshold for the aggregated trust value for a social
trust path in a trust network. If the aggregated trust value of a social trust path is
greater than the specified threshold, the trust path is kept for trust evaluation.
Moreover, existing trust path selection methods do not consider the social contexts,
83
84 Finding the Optimal Social Trust Path
including the social relationship between participants and the social position of partic-
ipants. These social contexts have significant influence on trust propagation [3, 102].
In addition, a source participant may have different purposes in evaluating the trust-
worthiness of the target participant, such as hiring employees, or introducing products.
Therefore, a source participant may have different social trust path selection crite-
ria, and thus, should be able to set certain constraints on the above social context in
trust path selection. However, such a capability is not supported by existing methods
[53, 77].
In this chapter, we first propose a novel concept, Quality of Trust (QoT), and mod-
els the multiple QoT constrained optimal social trust path selection problem as a Multi-
Constrained Optimal Path (MCOP) selection problem, which is proved to be NP-
Complete in [67]. Then, we propose an approximation algorithm, called MONTE K
based on the Monte Carlo method, and two heuristic algorithms, called H OSTP and
MFPB-HOSTP based on the Dijkstra’s shortest path algorithm and our novel search
strategies. The experimental results illustrate that the proposed methods outperform
the existing methods in both the quality of the identified social trust path and the exe-
cution time.
5.1 Quality of Trust (QoT) and QoT Attributes Aggre-
gation
5.1.1 Quality of Trust (QoT)
In Service-Oriented Computing (SOC), QoS (Quality of Service) consists of a set of
attributes, used to illustrate the ability of services to guarantee a certain level of per-
formance [40]. Similar to QoS, we propose a new concept, Quality of Trust.
Definition 3: Quality of Trust (QoT) is the ability to guarantee a certain level of trust-
worthiness in trust propagation along a social trust path, taking trust (T ), social inti-
macy degree (SI), and community impact factor (CIF ), as attributes.
§5.1 Quality of Trust (QoT) and QoT Attributes Aggregation 85
In service invocations, users can set multiple end-to-end constraints for the at-
tributes of QoS to satisfy their requirements (e.g., cost, delay and availability) of ser-
vices. Different requirements have different constraints (e.g., total cost<$20, delay<5s
and availability>70%). In our model, to satisfy different trust evaluation criteria, a
source participant can specify multiple end-to-end constraints for QoT attributes (i.e.,
T , SI and CIF ) as the requirements of trust propagation in a social trust path of
different domains.
Let Qµvs,vt
(µ ∈ {T, SI, CIF}) denote the end-to-end constraint of QoT attribute
µ for the paths between vs and vt in a certain domain (throughout this thesis, vs denotes
the source participant and vt denotes the target participant in a social network). For
example, as shown in Fig. 1.1, to hire employees, A, a retailer manager specifies
the end-to-end QoT constraints for the social trust paths from A to M as QA,M =
{QTA,M > 0.3, QSI
A,M > 0.3, QCIFA,M > 0.8}, if he/she believes the social position
of participants is more important in the domain of employment. But when looking
for new customers for selling products, A could specify QoT constraints as QA,M =
{QTA,M > 0.8, QSI
A,M > 0.3, QCIFA,M > 0.3}, if he/she believes the social relationships
between participants are more important in the domain of product sale.
5.1.2 QoT Attribute Aggregation
To specify end-to-end QoT constraints, we propose the QoT attribute aggregation
methods as follows.
5.1.2.1 Trust Aggregation
The trust values between a source participant and the target participant in a social path
can be aggregated based on trust transitivity property (i.e., if A trusts B and B trusts
C, then A trusts C to some extent) [48]. Since trust is discounted with the increase
of transitivity hops [23], in our model, we adopt the strategy proposed in [73, 124],
where if there are n participants a1, ..., an in order in a social trust path (denoted as
86 Finding the Optimal Social Trust Path
p(a1, ..., an)), the aggregated trust value in a certain domain is calculated as in Eq.
(5.1). This strategy has been widely used in the literature as a trust aggregation method
[10, 83, 124].
Tp(a1,...,an) =∏
(ai,ai+1)∈p(a1,...,an)
Tai ai+1(5.1)
This aggregated trust value will be combined with the social intimacy degree and
the community impact factor in the following context to select the optimal social trust
path.
5.1.2.2 Social Intimacy Degree Aggregation
Firstly, social intimacy between participants decays with the increasing number of
hops between them in a social trust path [72, 102]. In addition, in the real world, the
intimacy degree decays fast when its value approaches 1 (the slope approaches the
minimum). In contrast, the intimacy degree decays slowly when its value approaches
zero (the slope approaches the maximum) [18, 56]. Namely, the decay speed of the
social intimacy degree is non-linear in social networks. The aggregated SI value in
path p(a1, ..., an) can be calculated by Eq. (5.2) whose function image is a hyperbolic
curve, fitting the characteristic of social intimacy attenuation [102].
SIp(a1,...,an) =∏
(ai,ai+1)∈p(a1,...,an)
SIai ai+1(5.2)
5.1.2.3 Community Impact Factor Aggregation
As illustrated in social psychology [99], in the same society, the community impact
factor of a participant does not decay with the increase of transitivity hops in a certain
domain. Thus, the aggregated CIF value of p(a1,...an) in a certain domain can be
calculated by Eq. (5.3).
CIFp(a1,...,an) =
∑n−1i=2 CIFai
n− 2(5.3)
§5.2 The Proposed MONTE K for Optimal Social Trust Path Selection 87
5.1.3 Utility Function
In our model, we define the utility (denoted as F) as the measurement of the trustwor-
thiness of social trust paths. The utility function takes the QoT attributes T , SI and
CIF as the arguments in Eq. (5.4). The non-linearity of the trust and intimacy decay
between two non-adjacent individuals have been considered in the computation of the
utility function that is used in path selection.
Fp(a1,...,an) =ωT ∗ Tp(a1,...,an)+ωSI ∗ SIp(a1,...,an)+ωCIF ∗CIFp(a1,...,an) (5.4)
where ωT , ωSI and ωCIF are the weights of T , SI and CIF in domain i respectively;
0 < ωT , ωSI , ωCIF < 1 and ωT + ωSI + ωCIF = 1. A source participant can specify
different weights for different QoT attributes in path selection. For example, if a source
participant believes the social position of participants is more important in the domain
of employment, he/she can specify a relative high value for ωCIF . In contrast, if he/she
regards the social relationship is more important, he/she can specify a relatively high
value for ωSI .
A feasible path (solution) is the social trust path that can satisfy multiple end-to-
end QoT constraints. The goal of optimal social trust path selection is to select the
optimal path (solution) that yields the best utility with the weights specified by the
source participant from all feasible paths (solutions).
5.2 The Proposed MONTE K for Optimal Social Trust
Path Selection
The optimal social trust path selection with multiple end-to-end QoT constraints can
be modelled as the classical Multi-Constrained Optimal Path (MCOP) selection prob-
lem that is NP-Complete [67]. In this section, we first analyse some existing approx-
imation algorithms for the MCOP selection problem and then propose an efficient
88 Finding the Optimal Social Trust Path
approximation algorithm, MONTE K, based on the Monte Carlo method [43] and our
optimization strategies
5.2.1 Existing Approximation Algorithms
In the literature, several approximation algorithms have been proposed for the MCOP
selection problem.
Korkmaz et al. [67] propose a heuristic algorithm H MCOP for the multiple-
constrained optimal path selection in service invocation. In this algorithm, both multi-
constrained values and QoS attributes values are aggregated based on Eq. (5.5).
gλ(p) , (q1(p)
Q1vs,vt
)λ + (q2(p)
Q2vs,vt
)λ + ... + (qm(p)
Qmvs,vt
)λ (5.5)
where λ≥ 1; qi(p) is the aggregated value of the ith QoS attribute of path p (e.g.,
the total cost of the services in a path formed by service invocation); Qivs,vt
is the ith
QoS constraint value of the selected path between vs and vt (e.g., Qcostvs,vt
≤ $100).
H MCOP first adopts the Dijkstra’s shortest path algorithm [31] to find the path
with the minimum gλ from vt to vs, which intends to investigate whether there exists
a feasible solution satisfying all end-to-end QoS constraints in a sub-network. In this
process, at each intermediate node vk, the aggregated value of each QoS attribute for
the identified path from vk to vt is computed and recorded. If there exists at least one
feasible solution, then these aggregated values are used in another search from vs to
vt, which intends to identify a feasible path from vs to vt with the minimal cost of
services.
H MCOP was one of the most promising algorithms for the MCOP selection prob-
lem as it outperformed prior existing algorithms in both algorithm efficiency and solu-
tion quality [67].
Consequently, in the field of Service-Oriented Computing (SOC), Yu et al. [134]
propose an approximation algorithm, MCSP K to solve the quality-driven service se-
lection problem that is also the MCOP selection problem. This method keeps only K
§5.2 The Proposed MONTE K for Optimal Social Trust Path Selection 89
paths from a source node to each intermediate node, aiming to reduce the search space
and execution time. Their K-path selection is based on Eq. (5.6).
ξ(p) , max{( q1(p)
Q1vs,vt
), (q2(p)
Q2vs,vt
), ..., (qm(p)
Qmvs,vt
)} (5.6)
From Eq. (5.6), if any QoS attribute value does not satisfy the corresponding QoS
constraint in path p, then ξ(p) > 1. In their search strategies, the paths with up to K
minimum ξ values are kept at each intermediate node. This method never prunes any
feasible path if it exists. In their service candidate graph, all services are categorised
into different service sets based on their functionalities. Any two nodes in adjacent
service sets have a link with each other and thus all paths from a source node to an
intermediate node can be enumerated when necessary, avoiding an exhaustive search.
But if a network does not have such a typical structure, MCSP K has to search all paths
from a source to each intermediate node and hence the time complexity will become
exponential. Therefore, the algorithm does not fit large-scale social networks.
Some other algorithms [137, 138] adopt integer linear programming to solve the
service selection problem with multi-QoS constraints. But in [134] they have been
proved to have low efficiency in finding a near-optimal solution in large-scale net-
works.
5.2.2 Algorithm Description of MONTE K
In MONTE K, we adopt the following two optimization strategies.
Optimization Strategy 1: K-path selection. Let vs denote a source participant and
vt denote the target one. According to Eq. (5.6), the lower the ξ value of a path, the
higher the probability for that path to be a feasible solution. Thus, given a partially
identified social trust path from vs to vx (vx 6= vt), we calculate the ξ values of the
paths from vs to each neighboring node of vx and record up to K neighboring nodes
that yield up to K minimum ξ values as candidates for selection.
As this strategy selects no more than K neighbors at each step in social trust path
90 Finding the Optimal Social Trust Path
selection, it can reduce the search space and deliver higher efficiency than MCBA.
Optimization Strategy 2: Optimization at dominating nodes. If the indegree of
vy (vy 6= vs) is greater than 1 in the social network, then node vy is regarded as a
dominating node. To obtain a near-optimal solution, MONTE K performs multiple
simulations. In the first simulation, if a social trust path from vs to vy (denoted as path
p1) is selected, we store the utility F , ξ value and the aggregated value of each QoT
attribute of p1 at vy. In all subsequent simulations, if a different social path from vs to
vy (denoted as path py, where y > 1) is selected, the optimization is performed in the
following situations.
Situation 1: If vy = vt and F(py) < F(p1), it indicates py is worse than p1. Thus
we replace the values of py (i.e., T , SI , CIF , F and ξ) with the one stored at vy .
Situation 2: If vy = vt and F(py) > F(p1), it indicates py is better than p1. Thus,
we store the values of py at vy.
Situation 3: If vy 6= vt, F(py) < F(p1) and ξ(py) > ξ(p1), it indicates py is worse
than p1. Thus we replace the values of py with the one stored at vy .
Situation 4: If vy 6= vt, F(py) > F(p1) and ξ(py) < ξ(p1), it indicates py is better
than p1. Thus, we store the values of py at vy.
Following Strategy 2, the dominating node vy records T , SI , CIF , F and ξ values
of the locally optimal social trust path from vs to vy. The optimization at vy can
guarantee that the delivered solution from vs to vy is locally optimal.
5.2.3 The Process of MONTE K
Initialization: Mark the status of all nodes in the network as unvisited. Add vs into
set temp P that stores the solution (i.e., identified social trust path). Let Min K(vu)
be a set that stores up to K neighboring nodes of node vu (lines 1 to 3 in Algorithm 5).
Step 1: Get an unvisited node vu from temp P and mark vu as visited. Select up to
K neighboring nodes of vu based on strategy 1 and put these nodes into Min K(vu)
(lines 4 to 10 in Algorithm 5).
§5.2 The Proposed MONTE K for Optimal Social Trust Path Selection 91
Algorithm 5: MONTE KData: MT (vs, vt), QoT constraints, vs, vt, K-path numberResult: F , Pst
/*vs, vt: a source and the target participants; F : utility; Pst: identified social trust path; temp P : partly identifiedsocial trust path; deg−(v): the indegree of v; P(v): the probability of v to be selected; adj[vu]: neighboring nodes ofvu; Min K(vu): the set stores up to K neighboring nodes of vu; Fold(pv), ξold(pv), Told(pv), SIold(pv),CIFold(pv), tempold P (pv): values stored at dominating node v; */begin
1 Mark the status of all node as unvisited, Pst = ∅, temp P ←− vs;2 while (unvisited node exists in temp P ) do3 Get unvisited node vu from temp P4 Mark vu as visited;5 for each vi ∈ adj[vu] do6 Calculate T (pvi ), SI(pvi ), CIF (pvi ) and ξ(pvi )
end7 if size(adj[vu])> K then8 Put vi with K minimum ξ(pvi ) into Min K(vu);
end9 else
10 Put vi ∈ adj[vu] into Min K(vu);end
11 for each vi ∈ Min K(vu) do12 F(pvi ) = ωT ∗ T (pvi ) + ωSI ∗ SI(pvi ) + ωCIF ∗ CIF (pvi );
13 P(vi) = F(pvi ) /∑size(Min K(vu))
i=1 F(pvi );end
14 Generate a random number rand ∈ [0, 1];15 Select the mth node vj such that rand ≤ ∑m
i=1 P(vi);16 if ξ(pvj ) > 1 then17 Break;
end18 else19 if deg−(vj) > 1 then20 Optimization at Dominating Nodes (F(pvj ), ξ(pvj ), T (pvj ), SI(pvj ), CIF (pvj ),
temp P );end
21 if vj = vt then22 F = F(pvj ), Pst = temp P ;23 Return F and Pst;
end24 else25 T (pvj ) = Tnew(pvj ), SI(pvj ) = SInew(pvj );26 CIF (pvj ) = CIFnew(pvj ), temp P = temp Pnew;27 Put vj into temp P ;
endend
endend
92 Finding the Optimal Social Trust Path
Algorithm 6: Optimization at Dominating NodesData: F(pvj ), ξ(pvj ), v, temp P , T (pvj ), SI(pvj ), CIF (pvj )Result: Fnew(pvj ), ξnew(pvj ), temp Pnew , Tnew(pvj ), SInew(pvj ), CIFnew(pvj )
begin1 Get (node(vj).F , ξ, T, SI, CIF, temp P ) that stored at vj ;2 Put these values into (Fold(pvj ), ξold(pvj ), Told(pvj ), SIold(pvj ), CIFold(pvj ), temp Pold);3 if vj 6= vt then4 if F(pvj ) < Fold(pvj ) and ξ(pvj ) > ξold(pvj ) then5 Put {Fold(pvj ), ξold(pvj ), Told(pvj ), SIold(pvj ), CIFold(pvj ), temp Pold} into {Fnew(pvj ),
ξnew(pvj ), Tnew(pvj ), SInew(pvj ), CIFnew(pvj ), temp Pnew}end
6 else7 if F(pvj ) > Fold(pvj ) and ξ(v) < ξold(pvj ) then8 Put {F(pvj ), ξ(pvj ), T (pvj ), SI(pvj ), CIF (pvj ), temp P} into {Fnew(v), ξnew(v),
Tnew(v), SInew(v), CIFnew(v), temp Pnew};9 Update(node(vj).F , ξ, T, SI, CIF, temp P ) with these values;
endend
end10 else11 if F(pvj ) < Fold(pvj ) then12 Put {Fold(pvj ), ξold(pvj ), Told(pvj ), SIold(pvj ), CIFold(pvj ), temp Pold} into {Fnew(pvj ),
ξnew(pvj ), Tnew(pvj ), SInew(pvj ), CIFnew(pvj ), temp Pnew}end
13 else14 Put {F(pvj ), ξ(pvj ), T (pvj ), SI(pvj ), CIF (pvj ), temp P} into {Fnew(pvj ), ξnew(pvj ),
Tnew(pvj ), SInew(pvj ), CIFnew(pvj ), temp Pnew};15 Update (node(vj).F , ξ, T, SI, CIF, temp P ) with these values;
endend
16 Return(Fnew(pvj ), ξnew(pvj ), Tnew(pvj ), SInew(pvj ), CIFnew(pvj ), temp Pnew)end
Step 2: For each vi ∈ Min K(vu), calculate the probability of vi for selection,
based on the utility of the social trust path from vs to vi via vu (denoted as path pvi).
The probability of vi to be selected is P(pvi) =
F(pvi )∑size(Min K(vu))i=1 F(pvi )
(lines 11 to 13 in
Algorithm 5).
Step 3: Select vj from set Min K(vu) based on a random number rand ∈ [0, 1]
and {P(pvi)}. If ξ(pvj
) ≤ 1 and the indegree of vj is greater than 1, then vj is a
dominating node and thus performs the optimization at vj based on Strategy 2. If
ξ(pvj) > 1, it indicates that no feasible solution has been delivered in this simulation
(lines 14 to 27 in Algorithm 5 and lines 1 to 15 in Algorithm 6).
Step 4: If vj 6= vt, add vj into temp P and go to Step 1. If vj = vt, return temp P
and F(temp P ) (line 16 in Algorithm 6).
According to the power-law characteristic [103], only a few nodes have a large
§5.3 Experiments on MONTE K 93
outdegree in social networks (e.g., in Enron email corpus1, 94.7% nodes have an out-
degree less than 15). Therefore, in MONTE K, each node can keep a small search
space without pruning a large number of neighboring nodes (i.e., candidates) of a
node in K-path selection, which results in high efficiency and a higher probability of
finding the optimal solution. The time complexity of MONTE K is O(slmK), where
s is the number of simulations; l is the average length of the shortest social trust paths
from a source participant to the target one in social networks; m is the maximal outde-
gree of nodes in social networks and K is the argument specified for K-path selection.
In social networks, usually l < 7 according to the small-world characteristic [103].
Thus the time complexity of MONTE K is O(smK). By both addressing the charac-
teristics of social networks and adding optimization strategies in the algorithm design,
MONTE K can deliver better solutions with less execution time than existing methods.
5.3 Experiments on MONTE K
5.3.1 Experiment Settings
The Enron email dataset has been proved to possess the small-world and power-law
characteristics of social networks and has been widely used in the studies of social
networks [49, 96, 117]. In addition, the social intimacy degree between participants
and the community impact factor of participants can be calculated through mining the
subjects and contents of emails [96]. Therefore, in contrast to other real social network
datasets (e.g., Epinions1 and FilmTrust), the Enron email dataset fits our proposed
complex social network structure very well. Thus, to verify our proposed algorithm,
we select the Enron email corpus with 87,474 nodes (participants) and 30,0511 links
(formed by sending and receiving emails) as the dataset, and conduct experiments on
it.
As the complexity of MCSP K [134] is exponential in finding an optimal social
1http://epinions.com/
94 Finding the Optimal Social Trust Path
trust path in social networks, it is ignored in our experiments. Instead, we com-
pare MONTE K with H MCOP [67] and MCBA [73] in both execution time and
the utilities of identified social paths. Since this thesis does not focus on detailed
data mining techniques, in our experiments, the T , SI and CIF values are ran-
domly generated. The end-to-end QoT constraints are set as Qvs,vt = {QTvs,vt
≥0.05, QSI
vs,vt≥ 0.001, QCIF
vs,vt≥ 0.3} and the weights of attributes in utility function
are set as ωT = 0.25, ωSI = 0.25 and ωCIF = 0.5.
All three algorithms are implemented using Matlab R2008a running on an IBM
ThinkPad SL500 laptop with an Intel Core 2 Duo T5870 2.00GHz CPU, 3GB RAM,
Windows XP SP3 operating system and MySql 5.1.35 database.
5.3.2 Results and Analysis
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(d) 236 Nodes
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Figure 5.1: Maximal length of paths is 4 hops
In this experiment, in order to evaluate the performance of our proposed approx-
imation algorithm in the sub-networks of different scales and structures, we first ran-
domly select 16 pairs of source and target nodes from Enron email dataset. We then ex-
tract the corresponding 16 sub-networks between them by using the exhaustive search
method. Among them, the maximal length of a social trust path varies from 4 to 7
§5.3 Experiments on MONTE K 95
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(d) 286 Nodes
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Figure 5.2: Maximal length of paths is 5 hops
hops following the small-world characteristic. The properties of these sub-networks
are listed in Table 5.1.
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(d) 651 Nodes
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Figure 5.3: Maximal length of paths is 6 hops
The number of simulations of MONTE K and MCBA in each sub-network is also
listed in Table 5.1. The average outdegree in all these sub-networks is 3.77 and 95.5%
nodes have an outdegree less than 15. Hence we set K = 15 in the K-path selec-
96 Finding the Optimal Social Trust Path
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(b) 321 Nodes
Figure 5.4: Maximal length of paths is 7 hops
tion, without pruning a large number of neighboring nodes of most nodes following
the power-law characteristic [103]. Secondly, we perform 500 repeated experiments
for MONTE K and MCBA in each sub-network and record the utilities of the iden-
tified social trust paths in each experiment. The maximal utilities of the social trust
paths identified in all 500 experiments by MONTE K and MCBA are selected for
the comparison with that yielded by H MCOP. The average execution time of each
of MONTE K and MCBA in each sub-network is recorded based on 500 repeated
experiments. The execution time of H MCOP is averaged based on 5 independent
executions. The results are plotted in Fig. 5.1 to Fig. 5.4.
Utility: We can see that in any of 16 cases, MONTE K does not yield any utility
worse than that of H MCOP while in most sub-networks, the utilities of social trust
paths identified by MONTE K are better than those of H MCOP (see Fig. 5.1(a,
c, d), Fig. 5.2(a) to (d), Fig. 5.3 (a) to (d) and Fig. 5.4 (b) to (d)). The sum of
utilities computed by MONTE K is 12.23% more than that of H MCOP in 4 hops
sub-networks, 4.27% more in 5 hops, 60.62% more in 6 hops and 41.51% more in 7
hops. This is because when a trust path with the maximal utility is a feasible solution,
H MCOP can identify it as the optimal solution. However, when the identified trust
§5.3 Experiments on MONTE K 97
Table 5.1: Properties of different social networksID Max Number of Number of Max Max Simulation
Hops Nodes Links Outdegree Indegree Times1 4 60 113 16 15 1002 4 86 192 20 32 1003 4 115 257 41 82 1504 4 236 1321 74 91 2005 5 60 107 9 18 1006 5 215 528 34 48 2007 5 240 655 32 49 2508 5 286 749 31 84 3009 6 61 124 17 32 100
10 6 161 355 43 46 20011 6 371 1623 56 48 35012 6 651 2475 173 151 45013 7 137 373 48 18 20014 7 321 860 39 38 35015 7 551 3265 122 91 40016 7 793 3411 83 89 500
path is not a feasible solution, H MCOP can hardly find a near-optimal solution and
some times yields an infeasible one even when a feasible solution exists (see Fig.
5.3(b) where the utility computed by H MCOP is 0).
Regarding the utility of identified paths, MONTE K also outperforms MCBA in
most cases and is no worse than MCBA in all cases. The sum of utilities computed
by MONTE K is 17.25% more than that of MCBA in 4 hops sub-networks, 10.89%
more in 5 hops, 14.30% more in 6 hops and 34.60% more in 7 hops. This is because
Strategy 2 in MONTE K guarantees that the solutions identified by later simulations
will be no worse than the current one.
Execution Time: From Fig. 5.1 to Fig. 5.4, we can observe that the execution
time of MONTE K is significantly less than that of H MCOP in all sub-networks. The
total execution time of MONTE K is only 5.92% of that of H MCOP in 4 hops sub-
networks, 10.58% in 5 hops, 5.63% in 6 hops and 4.05% in 7 hops. In particular, in
the most complex sub-network with 793 nodes, 3411 links and 7 hops (see the last
row of Table 5.1), the execution time of MONTE K is only 2.88% of that of H MCOP
98 Finding the Optimal Social Trust Path
(see Fig. 5.4 (d)). From the above results, we can see that MONTE K is much more
efficient than H MCOP for identifying the optimal social trust path, especially in larger
scale sub-networks. (see Fig. 5.1(d), Fig. 5.2(c, d), Fig. 5.3(c, d) and Fig. 5.4(b) to
(d)).
In addition, the execution time of MONTE K is also less than MCBA. The total
execution time of MONTE K is 91.48% of that of MCBA in 4 hops sub-networks,
87.72% in 5 hops, 86.94% in 6 hops and 78.25% in 7 hops. This is because in
MONTE K, when any QoT constraint of a trust path from the source participant to an
intermediate node vk can not be satisfied, MONTE K starts a new simulation, rather
than searching the social trust path from v to the target. Thus, the execution time of
MONTE K is less than MCBA in all sub-networks. And the greater the number of
hops, the less the execution time of MONTE K than MCBA.
Through the above experiments conducted in the sub-networks with different scales
and structures, we can see that our proposed approximation algorithm, MONTE K,
addresses the characteristics of online social networks well and thus can deliver bet-
ter near-optimal solutions with less execution time than existing approximation algo-
rithms.
5.4 The Proposed H OSTP for Optimal Social Trust
Path Selection
In this section, we propose an efficient heuristic algorithm, H OSTP, for the QoT
constrained optimal social trust path selection. In H OSTP, we first adopt the Back-
ward Search procedure from the target (denoted as vt) to the source (denoted as vs)
to investigate whether there exists a feasible solution in the sub-network between vs
and vt, and record the aggregated QoT attributes (i.e., T, SI and CIF ) of the identi-
fied path from vt to each intermediate node vk. If a feasible solution exists, we then
adopt the Forward Search procedure to search the network from vs to vt to deliver a
§5.4 The Proposed H OSTP for Optimal Social Trust Path Selection 99
near-optimal solution.
5.4.1 Algorithm Description of H OSTP
In social trust path selection, if a path satisfies multiple QoT constraints, it means that
each aggregated QoT attribute (i.e., T , SI or CIF ) of that path should be larger than
the corresponding QoT constraint. Therefore, we propose an objective function in Eq.
(5.7) to investigate whether the aggregated QoT attributes of a path can satisfy the QoT
constraints in a certain domain. From Eq. (5.7), we can see that if any aggregated QoT
attribute of a social trust path does not satisfy the corresponding QoT constraint, then
δ(p) > 1. Otherwise δ(p) ≤ 1.
δ(p) , max{( 1− Tp
1−QTvs,vt
), (1− SIp
1−QSIvs,vt
), (1− CIFp
1−QCIFvs,vt
)} (5.7)
Backward Search: In the backward search from vt to vs, H OSTP identifies the
path ps from vt to vs with the minimal δ based on the Dijkstra’s shortest path algorithm
[31]. In the searching process, at each node vk (vk 6= vt), the path from vt to vk with
the minimal δ (denoted as pb(δ)vk→vt) is identified and T
pb(δ)vk→vt
SIp
b(δ)vk→vt
and CIFp
b(δ)vk→vt
are
recorded. According to the following Theorem 1, the Backward Search procedure can
investigate whether there exists a feasible solution in the sub-network.
Theorem 1: In the Backward Search procedure, the process of identifying the path
with the minimal δ can guarantee to find a feasible solution if one exists in a sub-
network.
Proof: Let ps be a path from vt to vs with the minimal δ, and p∗ be a feasible
solution. Then, δ(ps) ≤ δ(p∗). Assume ps is not a feasible solution, then ∃ϕ ∈{T, SI, CIF} that ϕps < Qϕ
vs,vt. Hence, δ(ps) > 1. Since p∗ is a feasible solution,
then δ(p∗) ≤ 1 and δ(ps) > δ(p∗). This contradicts δ(ps) ≤ δ(p∗). Therefore, ps is a
feasible solution. 2
The Backward Search procedure can always identify the path with the minimal δ.
If δmin > 1, it indicates there is no feasible solution in the sub-network. If δmin ≤ 1, it
100 Finding the Optimal Social Trust Path
indicates there exists at least one feasible solution and the identified path is a feasible
solution.
Forward Search: If there exists a feasible solution in the sub-network, a heuristic
forward search is executed from vs to vt. This process uses the information provided
by the above Backward Search to identify whether there is another path pt which
is better than the above returned path ps (i.e., F(pt) > F(ps)). In this procedure,
H OSTP first searches the path with the maximal F value from vs. Assume node
vn ∈ {neighboring nodes of vs} is selected based on the Dijkstra’s shortest path
algorithm. H OSTP calculates the aggregated QoT attribute values of the path from
vs to vn (denoted as path pf(u)vs→vn). Let p
b(δ)vn→vt denote the path from vn to vt iden-
tified in the Backward Search procedure, then a foreseen path from vs to vt via vn
(denoted as fpf(u)+b(δ)vs→vn→vt = p
f(u)vs→vn + p
b(δ)vn→vt) can be identified. Let h denote the
number of hops of path fpf(u)+b(δ)vs→vn→vt = p
f(u)vs→vn + p
b(δ)vn→vt . The aggregated QoS at-
tribute values of fpf(u)+b(δ)vs→vn→vt can be calculated as T
fpf(u)+b(δ)vs→vn→vt
= Tp
f(u)vs→vn
∗ Tp
b(δ)vn→vt
,
SIfp
f(u)+b(δ)vs→vn→vt
= (SIp
f(u)vs→vn
∗ SIp
b(δ)vn→vt
)/hα (α ≥ 1 is the argument for controlling the
attenuation speed of SI) and CIFfp
f(u)+b(δ)vs→vn→vt
= (CIFp
f(u)vs→vn
+ CIFp
b(δ)vn→vt
)/(h − 1).
According whether fpf(u)+b(δ)vs→vn→vt is feasible, H OSTP adopts the following searching
strategies.
Situation 1: If each aggregated QoT attribute of fpf(u)+b(δ)vs→vn→vt satisfies the corre-
sponding end-to-end QoT constraint, then H OSTP chooses the next node from vn
with the maximal F value which is calculated based on the Dijkstra’s shortest path
algorithm.
Situation 2: If any aggregated QoT attribute of fpf(u)+b(δ)vs→vn→vt does not satisfy the
corresponding end-to-end QoT constraint, then H OSTP does not search the path from
vn and the link vs → vn is deleted from the sub-network. Subsequently, H OSTP
performs the Forward Search procedure to search the path from vs in the sub-network
without the link vs → vn.
The following Theorem 2 illustrates that the social trust path pt identified by the
Forward Search procedure can not be worse than the feasible social trust path ps iden-
§5.4 The Proposed H OSTP for Optimal Social Trust Path Selection 101
Algorithm 7: H OSTPData: MT (vs, vt), QT
vs,vt, QSI
vs,vt, QCIF
vs,vt, vs, vt
Result: pt, F(pt)begin
1 ps = ∅, pt = ∅;2 Backward Search (MT (vs, vt), QT
vs,vt, QSI
vs,vt, QCIF
vs,vt, vs, vt);
3 if δ(ps) > 1 then4 Return no feasible solution;
end5 else6 Forward Search (MT (vs, vt), AQµ(p
b(δ)vk→vt ), QT
vs,vt, QSI
vs,vt, QCIF
vs,vt, vs, vt);
7 Return pt and F(pt);end
end
tified by the Backward Search procedure. Namely, F(pt) ≥ F(ps).
Theorem 2: With the social trust path ps identified by the Backward Search pro-
cedure and the social trust path pt identified by the Forward Search procedure in
H OSTP, if ps is a feasible solution, then pt is feasible and F(pt) ≥ F(ps).
Proof: Assume that path ps consists of n + 2 nodes vs, v′1, ..., v
′n, vt. In the For-
ward Search procedure, H OSTP searches the neighboring nodes of vs and chooses v1
from these nodes when a foreseen path from vs to vt via v1 is feasible and the current
path from vs to v1 has the maximal F . This step is repeated at all the nodes between
v1 and v′n until a social trust path pt is identified. If at each search step, only one
node (i.e., v1, ..., v′n) has a feasible foreseen path, then pt is the only feasible solution
in the sub-network between vs and vt. According to Theorem 1, then pt = ps. Thus,
F(pt) = F(ps). Otherwise, if pt 6= ps, It can lead to F(pt) > F(ps) by maximizing
the F value in all candidate nodes which have feasible foreseen paths based on the
Dijkstra’s shortest path algorithm. Therefore, Theorem 2 is correct. 2
If there exists only one feasible solution in the sub-network, it can be identified by
both the Backward Search procedure and the Forward Seach procedure, and it is the
optimal solution. Otherwise, if there exists more than one feasible solutions in the sub-
network, then the solution identified by the Forward Seach procedure is near-optimal
or optimal, which is better than the one identified by the Backward Search procedure.
102 Finding the Optimal Social Trust Path
Algorithm 8: Backward SearchData: MT (vs, vt), QT
vs,vt, QSI
vs,vt, QCIF
vs,vt, vs, vt
Result: ps
begin1 Set vx.δ = ∞ (vx 6= vt), vt.δ = 0, Sx = ∅;2 Add vt into Sx;3 while Sx 6= ∅ do4 va.δ = min(v∗a.δ) (v∗a ∈ Sx);5 for each vb ∈ adj[va] do6 h is the number of hops of the path from vt to vb;
7 δ(pb(δ)vb→vt ) = max[(1−AQT (p
b(δ)vb→vt ) ∗MT (va, vb).T/(1−QT
vs,vt), (1−AQSI(p
b(δ)vj→vt ) ∗
MT (va, vb).SI/hα)/(1−QSIvs,vt
), (1− (AQCIF (pb(δ)vj→vt ) + MT (va, vb).CIF ))/(h−
1)/(1−QCIFvs,vt
)];8 if vb /∈ Sx then9 Put vb into Sx;
10 prex(vb) = va;end
11 else if δ(pb(δ)vb→vt ) < AQvb.δ then
12 vb.δ = δ(pb(δ)vb→vt );
13 update AQµ(pb(δ)vb→vt );
14 Put vb into Sx;15 prex(vb) = va;
endend
16 Remove va from Sx;end
17 ps ← prex(vs) to prex(vt);18 Return ps
end
5.4.2 The Process of H OSTP
Step 1: Start the Backward Search procedure. Add vt into Sx. Select the node va
from Sx, where the δ value of the path from vt to va (i.e., pb(δ)va→vt) is the minimum of
all δ of the paths from vt to v∗a (v∗a ∈ Sx) (lines 1-2 in Algorithm 7 and lines 1 to 4 in
Algorithm 8).
Step 2: At each vb ∈ {neighboring nodes of va}, calculate δ value of the iden-
tified social trust path form vt to vb (denoted as pb(δ)vb→vt). If vb /∈ Sx, add vb into Sx.
Otherwise, if the current δ of vb less than the previous δ value recorded at vb, then
replace the stored δ with the current δ and record Tp
b(δ)vb→vt
, SIp
b(δ)vb→vt
and CIFp
b(δ)vb→vt
at
vb. Add vb into Sx and set prex(vb) = va (lines 5 to 15 in Algorithm 8).
Step 3: Remove va from Sx. If Sx 6= ∅, then go to Step 1. Otherwise return ps
through searching prex(vs). If δ(ps) ≤ 1, go to Step 3. Otherwise terminate (i.e., there
is no feasible solution in the sub-network) (lines 3 to 4 in Algorithm 7 and lines 16 to
§5.4 The Proposed H OSTP for Optimal Social Trust Path Selection 103
Algorithm 9: Forward SearchData: MT (vs, vt), QT
vs,vt, QSI
vs,vt, QCIF
vs,vt, vs, vt
Result: pt, F(pt)begin
1 Set F ′ = 1/F , vy .F ′ = ∞ (vy 6= vs), vs.F ′ = 0, Sy = ∅;2 Add vs into Sy ;3 while Sy 6= ∅ do4 vi.F ′ = min(v∗i .F ′) (v∗i ∈ Sy);5 for each vj ∈ adj[vi] do6 h′ is the number of the hops of the foreseen path from vs to vt via vj ;
7 tempT = AQT (pf(u)vs→vi
) ∗MT (vi, vj).T ∗AQT (pb(δ)vj→vt )
8 tempSI = AQSI(pf(u)vs→vi
) ∗MT (vi, vj).SI ∗AQSI(pb(δ)vj→vt )
9 tempCIF = AQCIF (pf(u)vs→vi
) + MT (vi, vj).CIF + AQCIF (pb(δ)vj→vt );
10 if tempT ≥ QTvs,vt
and tempSI/h′α ≥ QSIvs,vt
and tempCIF /(h′ − 1) ≥ QCIFvs,vt
then11 if vj /∈ Sy then12 Put vj into Sy ;13 prey(vj) = vi;
end14 else if F ′(pf(u)
vs→vj) < vj .F ′ then
15 vj .F ′ = F ′(pf(u)vs→vj
);
16 update AQµ(pf(u)vs→vj
);17 Put vj into Sy ;18 prey(vj) = vi;
endend
end19 Remove vi from Sy ;
end20 pt ← Prey(vt) to Prey(vs);21 Return pt and F(pt));
end
18 in Algorithm 8).
Step 4: Start the Forward Search procedure. Add vs into Sy. At each node
vy (vy 6= vs) in the sub-network, set vy.F = 0, and vs.F = ∞. Select the node
vi from Sy, where the 1/F value of the path from vs to vi (denoted as pi) is the mini-
mum in all 1/F values of the paths from vs to v∗i (v∗i ∈ Sy) (lines 5 to 6 in Algorithm
7 and lines 1 to 4 in Algorithm 9).
Step 5: At each vj ∈ {neighboring nodes of vi}, calculate F value of the identi-
fied path from vs to vj (denoted as pf(u)vs→vj ). If the current 1/F(p
f(u)vs→vj) is less than
the value recorded at node vj , then calculate each aggregated QoT attribute value
Tp
f(u)vs→vj
, SIp
f(u)vs→vj
and CIFp
f(u)vs→vj
. If each aggregated QoT value can satisfy the corre-
sponding QoT constraint, then replace the stored 1/F(pf(u)vs→vj) with the current 1/F(p
f(u)vs→vj)
at vj and set prey(vj) = vi. Otherwise, set MT (vi, vj).T = 0, MT (vi, vj).SI = 0 and
104 Finding the Optimal Social Trust Path
MT (vi, vj).CIF = 0 (lines 5 to 18 in Algorithm 9).
Step 6: Remove vi from Sx. If Sy 6= ∅, then go to Step 5. Otherwise, return pt
through searching array prey(vt) (line 7 in Algorithm 7 and lines 19 to 21 in Algorithm
9).
H OSTP consumes twice the execution time of Dijkstra’s shortest path algorithm.
The time complexity of H OSTP is O(NlogN+E), where N is the number of nodes in
the sub-network between vs and vt, and E is the number of links in the sub-network.
H OSTP has the same time complexity with H MCOP. But our proposed heuristic
algorithm has better searching strategies than H MCOP and thus outperforms it in both
efficiency and the quality of selected social trust paths (see a more detailed analysis in
section 6.4.2).
5.5 Experiments on H OSTP
5.5.1 Experiment Settings
As introduced in Section 4.4.1, Enron email dataset fit the proposed contextual trust-
oriented social network well. Thus, we also select the Enron email corpus with 87,474
nodes (participants) and 30,0511 links (formed by sending and receiving emails) as
the dataset for our experiments.
As we analysed in Section 5.2.1, H MCOP is the most promising algorithm for the
MCOP selection. Based on it, several approximation algorithms [74, 134] have been
proposed for the quality-driven service selection in the field of SOC. But they do not fit
the structure of large-scale complex social networks. Thus, to study the performance
of our proposed heuristic algorithm H OSTP, we compare it with H MCOP [67] in
both execution time and the utilities of identified social trust paths (see section 6.4.2).
In our experiments, the T , SI and CIF values are randomly generated. The argument
for controlling the attenuation speed is set as α = 1.5. The end-to-end QoT con-
straints specified by a source participant are set as Qvs,vt = {QTvs,vt
≥ 0.05, QSIvs,vt
≥
§5.5 Experiments on H OSTP 105
0 5 10 15 20 250
0.2
0.4
0.6
0.8
(a) ID of sub−network with 4 hops
Util
ity
0 5 10 15 20 250
0.2
0.4
0.6
0.8
(b) ID of sub−network with 5 hops
Util
ity
0 5 10 15 20 250
0.2
0.4
0.6
0.8
(c) ID of sub−network with 6 hops
Util
ity
0 5 10 15 20 250
0.2
0.4
0.6
0.8
(d) ID of sub−network with 7 hops
Util
ity
H_OSTPH_MCOP
S1: Same
S1: Same
S3: Feasible
S2: Better
S2: Better
S3: Feasible
S1: Same
S2: BetterS1: Same
S3: Feasible S3: Feasible
S2: Better
Figure 5.5: The comparison in path utilities of sub-networks
0.001, QCIFvs,vt
≥ 0.3} and the weights of attributes in the utility function specified by
the source participant are set as ωT = 0.25, ωSI = 0.25 and ωCIF = 0.5.
Both H OSTP and H MCOP are implemented using Matlab R2008a running on
an IBM ThinkPad SL500 laptop with an Intel Core 2 Duo T5870 2.00GHz CPU, 3GB
RAM, Windows XP SP3 operating system and MySql 5.1.35 database.
5.5.2 Results and Analysis
Table 5.2: The properties of the simplest and the most complex sub-networks in each group ofhops
HopsThe simplest sub-network The most complex sub-networkID Nodes Links ID Nodes Links
4 1 33 56 25 393 15435 1 49 90 25 680 26706 1 48 74 25 1300 63967 1 40 64 25 1695 11175
106 Finding the Optimal Social Trust Path
Table 5.3: The comparison of utility
AlgorithmsThe sum of utility
4 hops 5 hops 6 hops 7 hopsH OSTP 11.3515 10.4770 10.3937 9.7074H MCOP 10.5265 8.4712 6.6006 6.2363difference 10.78% more 12.37% more 15.75% more 15.57% more
Table 5.4: The comparison of execution time
AlgorithmsThe sum of execution time (sec)
4 hops 5 hops 6 hops 7 hopsH OSTP 133.9208 449.6327 1.1924e+003 2.2585e+003H MCOP 222.9832 875.9788 2.2262e+003 4.4913e+003difference 39.94% less 48.67% less 46.44% less 49.71% less
In this experiment, in order to evaluate the performance of our proposed heuristic
algorithm in the sub-networks of different scales and structures, we first randomly
select 100 pairs of source and target participants from the Enron email dataset1. We
then extract the corresponding 100 sub-networks between them by using the exhaustive
searching method. Among them, the maximal length of a social trust path varies from
4 to 7 hops following the small-world characteristic. These sub-networks are grouped
by the number of hops. In each group they are ordered by the number of nodes of
them. Table 5.2 list the properties of the simplest and the most complex sub-networks
in each group of hops. In the simplest case, the sub-network has 33 nodes and 56 links
(4 hops), while in the most complex case, the sub-network has 1695 nodes and 11175
links (7 hops). With each sub-network, we repeat the experiment 5 times for each of
H OSTP and H MCOP. The results are plotted in Fig. 5.5 and 5.6 where the execution
time of each of H OSTP and H MCOP is averaged based on the 5 independent runs.
Results (Utility). From Fig. 5.5, we can observe that in any case, our H OSTP
does not yield any utility worse than that of H MCOP (e.g., S1 in Fig. 5.5 (a) to (d))
while in most sub-networks (i.e., 59% of total sub-networks), the utilities of social
trust paths identified by H OSTP are better than those of H MCOP (e.g., S2 in Fig.
5.5 (a) to (d)). The sum of utilities computed by H OSTP and H MCOP in the sub-
§5.5 Experiments on H OSTP 107
0 5 10 15 20 250
20
40
60
80
ID of the sub−networks with 4 hops
Exe
cutio
n T
ime
(Sec
)
0 5 10 15 20 250
50
100
150
200
250
ID of the sub−networks with 5 hops
Exe
cutio
n T
ime
(Sec
)
0 5 10 15 20 250
200
400
600
800
1000
ID of the sub−networks with 6 hops
Exe
cutio
n T
ime
(Sec
)
0 5 10 15 20 250
500
1000
1500
ID of the sub−networks with 7 hops
Exe
cutio
n T
ime
(Sec
)
H_OSTPH_MCOP
Figure 5.6: The comparison in Execution time
networks with each group of hops is listed in Table 5.3. From the Table, we can see
that the sum of utilities of our proposed heuristic algorithm is 10.78% more than that
of H MCOP in 4 hops sub-networks, 12.37% more in 5 hops, 15.75% more in 6 hops
and 15.57% more in 7 hops.
Analysis (Utility). From the above results, we can see that H OSTP can yield a
better social trust path than H MCOP in most cases. This is because when a social trust
path with the maximal utility is a feasible solution in a sub-network, both H MCOP
and H OSTP can identify it as the optimal solution. Thus, they can identify the same
social trust path with the same utility. However, when the social trust path with the
maximal utility is not a feasible solution, H MCOP stops searching the path with the
minimum cost and consequently start searching the social trust path with the minimum
gλ (λ > 1). This heuristic search strategy can hardly find a near-optimal solution and
sometimes returns an infeasible one even when a feasible solution exists (e.g., S3 in
Fig. 5.5 (a) to (d)). In contrast, as illustrated by Theorem 1, H OSTP can identify a
108 Finding the Optimal Social Trust Path
feasible solution if it exists (e.g., S3 in Fig. 5.5 (a) to (d)). In addition, as illustrated by
Theorem 2, H OSTP can identify a near-optimal social trust path satisfying the end-to-
end QoT constraints if it exists. Therefore, in this case, the quality of the social trust
path identified by H OSTP is better than H MCOP.
Results (Execution Time). From Fig. 5.6, we can observe that the execution time
of H OSTP is less than that of H MCOP in all sub-networks. The total execution time
of each of H OSTP and H MCOP in each group of hops is listed in Table 5.4. From
the table, we can see that the total execution time of our proposed heuristic algorithm
is only 60.06% of that of H MCOP in 4 hops sub-networks, 51.33% in 5 hops, 53.56%
in 6 hops and 50.29% in 7 hops.
Analysis (Execution Time). From the above results, we can see that H OSTP
is much more efficient than H MCOP. The reasons are twofold. Firstly in the For-
ward Search procedure, H OSTP does not calculate gλ (λ > 1) which consumes a
large amount of execution time when λ → ∞ [74]. Secondly, in the searching pro-
cess, when any aggregated QoT attribute of a selected path from vs to vy (vy 6= vt)
does not satisfy the corresponding QoT constraint, node vy is not regarded as a candi-
date to be selected in the next searching step, which can reduce the search space and
thus significantly save the execution time.
Through the above experiments conducted in sub-networks with different scales
and structures, we can see that overall H OSTP is superior to H MCOP in both the
execution time and the quality of selected social trust path.
5.6 The Proposed MFPB-HOSTP for Optimal Social
Trust Path Selection
5.6.1 The Advantage and Disadvantage of H OSTP
Advantage: H OSTP could detect whether there exist a feasible solution in a sub-
network, as it adopts a new objective function δ(p) which is better than that of H MCOP.
§5.6 The Proposed MFPB-HOSTP for Optimal Social Trust Path Selection 109
If there exists at least one feasible solution, H OSTP does not deliver any solution
which is worse in quality than that of H MCOP, and could possibly deliver better so-
lutions than H MCOP. In addition, when a foreseen path is infeasible (i.e., at least one
aggregated QoT attribute value of the path does not satisfy the corresponding QoT
constraint), the corresponding link between nodes is deleted, which reduces the search
space and makes H OSTP more efficient than H MCOP [78].
Disadvantage: Although H OSTP significantly outperforms existing approxima-
tion algorithms in both the efficiency and the quality of identified social trust paths,
it still has a disadvantage called the imbalance problem of QoT attributes, which may
cause a failed feasibility estimation of a foreseen path in the forward search procedure
from vs to vt, and deliver a solution with a low utility that is not near optimal. We
analyse the disadvantage of H OSTP below in detail.
If a feasible solution (i.e., a path where the aggregated value of each QoT attribute
satisfies the corresponding QoT constraint) exists in the sub-network between vs and
vt, H OSTP performs the Forward Search procedure, where H OSTP investigates the
feasibility of the foreseen path fpf(u)+b(δ)vs→vk→vt to estimate whether a feasible solution can
be delivered by following pf(u)vs→vk . But this strategy may give a failed feasibility estima-
tion. Namely, even if fpf(u)+b(δ)vs→vk→vt is infeasible, there may still exist a feasible solution
identified by following pf(u)vs→vk in the sub-network.
We use the following example to illustrate the imbalance problem of QoT attributes
in H OSTP. Fig. 5.7 depicts a social network between vs and vt, which contains five
intermediate nodes v1 to v5, and the aggregated QoT attribute values computed by the
Backward Search procedure at each of these nodes is listed in Table 5.5. Suppose
that vs specifies the QoT constraints as QTvs,vt
> 0.3, QSIvs,vt
> 0.3 and QCIFvs,vt
> 0.2.
Based on the search strategy introduced in Section 5.4, at v4, H OSTP concatenates
the social trust path pf(u)vs→v4 with p
b(δ)v4→vt to form a foreseen path fp
f(u)+b(δ)vs→v4→vt with the
aggregated QoT attributes values as T = 0.2, SI = 0.48 and CIF = 0.5, which is
infeasible (note: the aggregated T = 0.2 does not satisfy the corresponding constraint
QTvs,vt
> 0.3). In such a situation, H OSTP deletes the link v2 → v4 in pf(u)vs→v4 and
110 Finding the Optimal Social Trust Path
Figure 5.7: Limitation of H OSTP
Table 5.5: Social trust paths and the aggregated QoT attributes valuesPath Nodes and Links T SI CIF
pf(u)vs→v4 vs → v1 → v2 → v4 0.4 0.8 0.5
pb(δ)v4→vt v4 → v3 → v5 → vt 0.5 0.6 0.5
pb(T )v4→vt v4 → vt 0.8 0.45 0.5
path v2 → vt v2 → vt 0.75 0.4 0.4
selects another path vs → v1 → v2 → vt as the near-optimal social trust path between
vs and vt. Suppose the QoT attributes have the same weights in the utility function,
then the utility of this path is 0.35.
However, as shown in Fig. 5.7, the aggregated values of QoT attributes of another
path v4 → vt (denoted as pb(T )v4→vt) are T = 0.8, SI = 0.45 and CIF = 0.5. If we
concatenate pf(u)vs→v4 and p
b(T )v4→vt together, a new foreseen path fp
f(u)+b(T )vs→v4→vt is formed that
is feasible. In such a situation, the path vs → v1 → v2 → v4 → vt with a utility of
0.39 is selected as the solution, which has a better quality than the one identified by
H OSTP (i.e., the utility=0.35).
From the above example, we can see that the foreseen path formed by concatenat-
ing path pf(u)vs→vk with path p
b(δ)vk→vt may not accurately estimate whether there exists a
feasible a solution identified by following pf(u)vs→vk in the forward search procedure. This
is because during searching pb(δ)vk→vt , one of the aggregated values of the QoT attributes
may be already close to the corresponding QoT constraints (e.g., T = 0.5 of pb(δ)v4→vt in
Fig. 5.7). In such a situation, if the aggregated values of that QoT attribute is also close
§5.6 The Proposed MFPB-HOSTP for Optimal Social Trust Path Selection 111
to the corresponding QoT constraint in pf(u)vs→vk (e.g., T = 0.4 of p
f(u)v4→vt in Fig. 5.7),
the foreseen path at vk is usually infeasible. This is the typical imbalance problem of
QoT attributes (e.g., the imbalance problem of T at v4 in Fig 5.7), which may lead to
a failed feasibility estimation of a foreseen path. In such a situation, H OSTP cannot
identify a social trust path with a high utility that is near-optimal.
5.6.2 Algorithm Description of MFPB-HOSTP
We first introduce some definitions below that are used to describe our algorithm.
Definition 4: (Backward Local Path (BLP)): In a sub-network from vs to vt, a Back-
ward Local Path (BLP) is the path from vt to an intermediate node vk, identified by the
backward search from vt to vs.
Based on Definition 5, path pb(δ)vk→vt identified by the backward search procedure is
a BLP.
Definition 5: (Forward Local Path (FLP)): In a sub-network from vs to vt, a For-
ward Local Path (FLP) is the path from vs to an intermediate node vk, identified by the
forward search from vs to vt.
Based on Definition 6, path pf(u)vs→vt identified by the forward search procedure is an
FLP. A foreseen path can be formed at the same intermediate node vk by concatenating
an FLP that ends at node vk and a BLP that starts from node vk.
Definition 6: (Composite Backward Local Path (CBLP)): in a sub-network be-
tween vs and vt, a Composite Backward Local Path (CBLP) is the path which is
composed of the BLP with the minimal δ and the links of BLP with the maximal
aggregated value for one of the QoT attributes.
Based on the above definitions, we propose a novel Multiple Foreseen Path-Based
Heuristic algorithm for Optimal Social Trust Path selection (MFPB-HOSTP) in com-
plex social networks that inherits the advantages of H OSTP (i.e., the objective func-
tion) and aims to overcome its disadvantage (i.e., the imbalance problem of QoT at-
tributes). Our MFPB-HOSTP also bidirectionally searches a sub-network (i.e., by
112 Finding the Optimal Social Trust Path
employing both a backward search and a forward search procedure) by adopting the
Dijkstra’s shortest path algorithm [31]. But our algorithm employs different search
strategies with H OSTP.
In the backward search procedure from vt to vs, at each intermediate node vk, in
addition to BLP pb(δ)vk→vt , MFPB-HOSTP first identifies the BLPs with the maximal ag-
gregated T , SI and CIF values respectively (denoted as pb(µ)vk→vt , µ ∈ {T, SI, CIF}).
When facing with the imbalance problem of QoT attribute µ at vk (e.g., T at v4 in
Fig. 5.7), the identified BLPs pb(µ)vk→vt are concatenated with the identified FLP, form-
ing other foreseen paths (e.g., fpf(u)+b(T )vs→v4→vt in Fig. 5.7), helping avoid a failed fea-
sibility estimation of a foreseen path and having a chance to deliver a better solu-
tion than H OSTP (e.g., the path vs → v1 → v2 → v4 → vt in Fig. 5.7). How-
ever, greedily maximizing the aggregated value of the QoT attribute may cause a new
imbalance problem of QoT attributes (see a detailed analysis in Step 2 in the fol-
lowing section of Algorithm Description). Therefore, MFPB-HOSTP then identifies
some CBLPs the number of which depends on the number of intermediate nodes of
pb(µ)vk→vt (µ ∈ {T, SI, CIF}). When facing with the new imbalance problem of QoT
attributes at vk, these CBLPs are used to be concatenated with the FLP to balance QoT
attributes in the newly formed foreseen paths, which could increase the probability of
delivering a solution with high utility that is near-optimal (see a detailed analysis in
Step 2 in the following section of Algorithm Description).
The backward search procedure could illustrate whether there exists a feasible so-
lution in a sub-network (it is proved in Theorem 1 in the following section of Algorithm
Description). If there exists at least one feasible solution, MFPB-HOSTP performs a
forward search procedure from vs to vt. This procedure intends to identify the path
with the maximal utility by using the Dijkstra’s shortest path algorithm [31]. When
facing with the imbalance problem of QoT attributes at vk, MFPB-HOSTP concate-
nates the FLP (i.e., pf(u)vs→vk) with BLPs and CBLPs, forming multiple foreseen paths,
instead of one foreseen path only in H OSTP. This strategy could effectively help ad-
dress the imbalance problem of QoT attributes in path selection, and thus helping avoid
§5.6 The Proposed MFPB-HOSTP for Optimal Social Trust Path Selection 113
a failed feasibility estimation of a foreseen path in the social path selection.
5.6.3 The Process of MFPB-HOSTP
In this section, we give a more detailed description of our proposed MFPB-HOSTP
algorithm.
Backward Search: In the Backward Search procedure, MFPB-HOSTP searches
the sub-network from vt to vs to investigate whether there exists a feasible solution
in the sub-network. In this process, at each intermediate node vk, several BLPs and
CBLPs from vt to vk are identified. The identification of these paths can be divided
into the following 4 steps.
Algorithm 10: MFPB-HOSTPData: MT (vs, vt), QT
vs,vt, QSI
vs,vt, QCIF
vs,vt
Result: pforwardvs→vt , F(pforward
vs→vt )begin
pforwardvs→vt = ∅, pbackward
vs→vt= ∅;
Backward Search(MT (vs, vt), QTvs,vt
, QSIvs,vt
, QCIFvs,vt
);if δ(pbackward
vs→vt) > 1 then
Return no feasible solution;endelse
Forward Search(MT (vs, vt), AQµ(pb(δ)vk→vt ), AQµ(p
b(µ)vk→vt ), AQµ(p
CBLP (µ)vk→vt ),
µ ∈ {T, SI, CIF}, QTvs,vt
, QSIvs,vt
, QCIFvs,vt
);
Return pforwardvs→vt and F(pforward
vs→vt );end
end
Step 1 (identify the BLP with the minimal δ): In social trust path selection, if a
path satisfies multiple QoT constraints, the aggregated value of each QoT attribute (i.e.,
T , SI or CIF ) of that path should be larger than the corresponding QoT constraint.
From Eq. (5.7), we can see that if any aggregated QoT attribute value of a social trust
path does not satisfy the corresponding QoT constraint, then δ(p) > 1. Otherwise
δ(p) ≤ 1.
To investigate whether there exists a feasible solution in a sub-network, in this step,
MFPB-HOSTP identifies the path from vt to vs with the minimal δ (i.e., pb(δ)vs→vt) based
on the Dijkstra’s shortest path algorithm [31]. In the searching process, at each in-
114 Finding the Optimal Social Trust Path
Algorithm 11: Backward Search ()Data: MT (vs, vt), QT
vs,vt, QSI
vs,vt, QCIF
vs,vt
Result: δ(pbackwardvs→vt
), AQµ(pb(δ)vk→vt ), AQµ(p
b(µ)vk→vt ), AQµ(p
CBLP (µ)vk→vt ), (µ ∈ {T, SI, CIF})
beginSet vx.d = ∞ (vx 6= vt), vt.d = 0, Sx = ∅, p
b(δ)vt→vt = vt;
Add vt into Sx;while Sx 6= ∅ do
va.d = min(v∗a.d) (v∗a ∈ Sx);for each vb ∈ adj[va] do
if vb /∈ Sx thenPut vb into Sx;
pb(δ)vb→vt = vb → va + p
b(δ)va→vt ;
endelse if δ(vb → va + p
b(δ)va→vt ) < vb.d then
Update vb.d and AQµ(pb(δ)vb→vt ), (µ ∈ {T, SI, CIF});
pb(δ)vb→vt = vb → va + p
b(δ)va→vt ;
endendRemove va from Sx;
endpbackward
vs→vt= p
b(δ)vs→vt ;
if δ(pbackwardvs→vt
) ≤ 1 thenComputing Max T (MT (vs, vt), QT
vs,vt, QSI
vs,vt, QCIF
vs,vt);
Computing Max SI(MT (vs, vt), QTvs,vt
, QSIvs,vt
, QCIFvs,vt
);Computing Max CIF (MT (vs, vt), QT
vs,vt, QSI
vs,vt, QCIF
vs,vt);
endend
termediate node vk, BLP pb(δ)vk→vt is identified and the aggregated QoT attribute values
of these paths (i.e., Tp
b(δ)vk→vt
SIp
b(δ)vk→vt
and CIFp
b(δ)vk→vt
) are computed and recorded. Ac-
cording to the Theorem 1 in H OSTP, the Backward Search procedure can investigate
whether there exists a feasible solution in the sub-network.
The Backward Search procedure of MFPB-HOSTP can always identify the path
with the minimal δ. If δmin > 1, it indicates there is no feasible solution in the sub-
network, then the algorithm terminates. If δmin ≤ 1, it indicates there exists at least
one feasible solution and the identified path is a feasible solution. In such a case, the
algorithm will perform the following steps to deliver a near-optimal solution.
Step 2 (identify the BLP with the maximal aggregated T value and the cor-
responding CBLPs): In this step, at each intermediate node vk, MFPB-HOSTP first
identifies the BLP with the maximal aggregated T value (i.e., pb(T )vk→vt), and then iden-
tifies several corresponding CBLPs which are composed of part of pb(T )vk→vt and a BLP
with the minimal δ from vt to each intermediate node in pb(T )vk→vt .
§5.6 The Proposed MFPB-HOSTP for Optimal Social Trust Path Selection 115
Figure 5.8: Multiple CBLPs in backward search procedure
Figure 5.9: The CBLP in path selection
(a): identify the BLPs with the maximal T . MFPB-HOSTP first identifies the
path from vt to vs with the maximal aggregated T value (i.e., pb(T )vs→vt) based on the
Dijkstra’s shortest path algorithm [31]. In the searching process, at each intermedi-
ate node vk, BLP pb(T )vk→vt (e.g., BLP v4 → vt in Fig. 5.7) and the aggregated QoT
attributes’ values of pb(T )vk→vt are computed and recorded. When facing with the imbal-
ance problem of T at vk, BLP pb(T )vk→vt is concatenated with the FLP p
f(u)vk→vt , forming
a new foreseen path fpf(u)+b(T )vs→vk→vt (e.g., the foreseen path v1 → v2 → v4 → vt in Fig.
5.7). This foreseen path could be used as a reference to estimate whether there exists a
feasible solution identified by following pf(u)vs→vk . This strategy could help avoid a failed
feasibility estimation of a foreseen path caused by the imbalance problem of T at vk.
(b): identify the CBLPs based on the BLPs with the maximal T . Greedily
maximizing the aggregated T value without considering other QoT attributes values in
pb(T )vk→vt may lead to the new imbalance problem of QoT attributes (i.e., SI and CIF ).
Therefore, in addition to pb(T )vk→vt , suppose there are M intermediate nodes (denoted as
116 Finding the Optimal Social Trust Path
Table 5.6: BLPs, CBLPs, and the aggregated QoT attributes valuesPath Nodes and Links T SI CIF
pf(u)vs→v2 vs → v1 → v2 0.3 0.8 0.5
pb(δ)v2→vt v2 → v4 → vt 0.25 0.5 0.4
pb(T )v2→vt v2 → v5 → v4 → vt 0.7 0.1 0.3
pCBLP 1(T )v2→vt v2 → v5 → vt 0.5 0.2 0.3
path v3 → vt v3 → v6 → vt 0.4 0.2 0.3
vl, l ∈ [1,M ]) in path pb(T )vk→vt , MFPB-HOSTP then identifies M Composite Backward
Local Paths at vk (denoted as pCBLP M (T )vk→vt which are composed of p
b(T )vk→vl l ∈ [1,M ] and
pb(δ)vl→vt , l ∈ [1,M ]. For example, as shown in Fig. 5.8, since there is no intermediate
node between v4 and vt in BLP pb(T )v4→vt (i.e., M=0), MFPB-HOSTP only identifies one
BLP pb(T )v4→vt = v4 → vt. Since there exists an intermediate node v4 between v2 and vt
in BLP pb(T )v2→vt (i.e., M = 1), in addition to p
b(T )v2→vt , MFPB-HOSTP identifies one CBLP
pCBLP 1(T )v2→vt = (v2 → v4) + p
b(δ)v4→vt . Similarly, at v1 there exist two intermediate nodes
between v1 and vt in BLP pb(T )v1→vt (i.e., M = 2), MFPB-HOSTP identifies two CBLPs.
They are CBLP pCBLP 1(T )v1→vt = (v1 → v2 → v4) + p
b(δ)v4→vt and CBLP p
CBLP 2(T )v1→vt =
(v1 → v2) + pb(δ)v2→vt . When facing with the new imbalance caused by the BLP with the
maximal T , the M CBLPs at vk are concatenated with the FLP pf(u)vs→vk . This strategy
could help avoid a failed feasibility estimation of a foreseen path caused by the new
imbalance problem of other two QoT attributes (i.e., SI and CIF ) at vk. Next we
use an example to illustrate the effectiveness of CBLPs in solving the new imbalance
problem of QoT attributes.
Fig. 5.9 depicts a sub-network between vs and vt. Table 5.6 lists the FLP at v2, the
BLP at v2, the corresponding CBLP at v2, and the aggregated values of QoT attributes
of these paths. Suppose that the QoT constraints specified by source participant vs
are QTvs,vt
= 0.12, QSIvs,vt
= 0.15 and QCIFvs,vt
= 0.3. We could see that the foreseen
path fpf(u)+b(δ)vs→v2→vt is infeasible due to the imbalance problem of T at v2 (T = 0.075 <
QTvs,vt
= 0.12). Then MFPB-HOSTP concatenates the FLP with BLP pb(T )v2→vt to form
another foreseen path fpf(u)+b(T )vs→v2→vt .
§5.6 The Proposed MFPB-HOSTP for Optimal Social Trust Path Selection 117
Algorithm 12: Computing Max T ()Data: MT (vs, vt), QT
vs,vt, QSI
vs,vt, QCIF
vs,vt
Result: AQµ(pb(T )vk→vt ) and AQµ(p
CBLP (T )vk→vt ), (µ ∈ {T, SI, CIF})
beginSet vx.d = ∞ (vx 6= vt), vt.d = 0, Sx = ∅, p
b(T )vt→vt = vt, p
CBLP (T )vt→vt = vt;
Add vt into Sx;while Sx 6= ∅ do
va.d = min(v∗a.d) (v∗a ∈ Sx);for each vb ∈ adj[va] do
obj = 1/AQT (pb(δT )va→vt + va → vb);
if vb /∈ Sx thenPut vb into Sx;
pb(T )vb→vt = vb → va + p
b(T )va→vt ;
endelse if obj < vb.d then
Update AQT (pb(T )vb→vt );
vb.d = obj;
pb(T )vb→vt = vb → va + p
b(T )va→vt ;
endfor i = 1 to M do
pCBLP i(T )vb→vt = p
CBLP i(T )va→vt ;
AQµ(pCBLP i(T )vb→vt ) = AQµ(p
CBLP i(T )va→vt );
end
pCBLP M+1(T )vb→vt = vb → va + p
b(δ)va→vt ;
endRemove va from Sx;
endend
However, we could see there arises a new imbalance problem of SI , where the
aggregated SI value of fpf(u)+b(T )vs→v2→vt does not satisfy the corresponding QoT constraint
(r = 0.08 < QSIvs,vt
= 0.15) and thus the foreseen path is infeasible. In such a situation,
suppose pb(δ)v5→vt = v5 → vt, at v2, MFPB-HOSTP identifies the CBLP p
CBLP 1(T )v2→vt =
v2 → v5 → vt and concatenates it with the FLP to balance the aggregated SI value.
In such a situation, the foreseen path fpf(u)+CBLP 1(T )vs→v2→vt is feasible. Assume the QoT
attributes have the same weight in the utility function, with the assistance of CBLP
pCBLP 1(T )v2→vt , MFPB-HOSTP could select the path vs → v1 → v2 → v5 → vt with the
utility of 0.117 as the solution. Otherwise, the path vs → v1 → v3 → v6 → vt with
the utility of 0.107 will be selected, which is worse than the one (i.e., utility is 0.117)
identified with the assistance of CBLPs.
From this example, we could see that when facing with the new imbalance problem
of QoT attributes caused by greedily maximizing the aggregated QoT attributes val-
118 Finding the Optimal Social Trust Path
Algorithm 13: Computing Max SI ()Data: MT (vs, vt), QT
vs,vt, QSI
vs,vt, QCIF
vs,vt
Result: AQµ(pb(SI)vk→vt ) and AQµ(p
CBLP (SI)vk→vt ), (µ ∈ {T, SI, CIF})
beginSet vx.d = ∞ (vx 6= vt), vt.d = 0, Sx = ∅, p
b(r)vt→vt = vt, p
CBLP (r)vt→vt = vt;
Add vt into Sx;while Sx 6= ∅ do
va.d = min(v∗a.d) (v∗a ∈ Sx);for each vb ∈ adj[va] do
obj = 1/AQSI(pb(δSI )va→vt + va → vb);
if vb /∈ Sx thenPut vb into Sx;
pb(SI)vb→vt = vb → va + p
b(SI)va→vt ;
endelse if obj < vb.d then
Update AQr(pb(r)vb→vt );
vb.d = obj;
pb(SI)vb→vt = vb → va + p
b(SI)va→vt ;
endfor i = 1 to M do
pCBLP i(SI)vb→vt = p
CBLP i(SI)va→vt ;
AQµ(pCBLP i(SI)vb→vt ) = AQµ(p
CBLP i(SI)va→vt );
end
pCBLP M+1(SI)vb→vt = vb → va + p
b(δ)va→vt ;
endRemove va from Sx;
endend
ues in BLPs, CBLPs could help avoid a failed feasibility estimation caused by a new
imbalance problem of QoT attributes. Thus with the assistance of CBLPs, MFPB-
HOSTP could deliver a better solution in some cases. In the process of identifying
these BLPs and CBLPs, if there exist two overlapping paths (i.e., they have the same
aggregated QoT attributes values), MFPB-HOSTP keeps only one of them for further
search, saving execution time.
Step 3 (identify the BLP with the maximal aggregated SI value and the cor-
responding CBLPs):
(a): identify the BLPs with the maximal SI . Similar to Step 2, in order to
avoid the imbalance problem of SI , in this step, at each intermediate node vk, MFPB-
HOSTP first identifies the BLP with the maximal aggregated SI value (denoted as
pb(SI)vk→vt) based on the Dijkstra’s shortest path algorithm [31]. In this search process,
at vk, the aggregated values of QoT attributes of pb(SI)vk→vt are computed and recorded.
§5.6 The Proposed MFPB-HOSTP for Optimal Social Trust Path Selection 119
Algorithm 14: Computing Max CIF ()Data: MT (vs, vt), QT
vs,vt, QSI
vs,vt, QCIF
vs,vt
Result: AQµ(pb(CIF )vk→vt ) and AQµ(p
CBLP (CIF )vk→vt ), (µ ∈ {T, SI, CIF})
beginSet vx.d = ∞ (vx 6= vt), vt.d = 0, Sx = ∅, p
b(CIF )vt→vt = vt, p
CBLP (CIF )vt→vt = vt;
Add vt into Sx;while Sx 6= ∅ do
va.d = min(v∗a.d) (v∗a ∈ Sx);for each vb ∈ adj[va] do
obj = 1/AQCIF (pb(δr)va→vt + va → vb);
if vb /∈ Sx thenPut vb into Sx;
pb(CIF )vb→vt = vb → va + p
b(CIF )va→vt ;
endelse if obj < vb.d then
Update AQCIF (pb(CIF )vb→vt );
vb.d = obj;
pb(CIF )vb→vt = vb → va + p
b(CIF )va→vt ;
endfor i = 1 to M do
pCBLP i(CIF )vb→vt = p
CBLP i(CIF )va→vt ;
AQµ(pCBLP i(CIF )vb→vt ) = AQµ(p
CBLP i(CIF )va→vt );
end
pCBLP M+1(CIF )vb→vt = vb → va + p
b(δ)va→vt ;
endRemove va from Sx;
endend
Algorithm 15: Path Selection ()Data: MT (vs, vt), Sy , va, vb
Result: pf(u)vs→vb
, AQµ(pf(u)vs→vb
), µ ∈ {T, SI, CIF}begin
if vb /∈ Sy thenPut vb into Sy and p
f(u)vs→vb
= pf(u)vs→va + va → vb;
endelse if 1/F(p
f(u)vs→va + va → vb) < vb.d then
Update AQµ(pf(u)vs→vb
);
pf(u)vs→vb
= pf(u)vs→va + va → vb;
endend
When facing with the imbalance problem of SI at vk, BLP pb(SI)vk→vt is concatenated
with the FLP pf(u)vs→vk , forming a new foreseen path fp
f(u)+b(SI)vs→vk→vt . This foreseen path
is used as a reference to estimate whether there exists a feasible solution identified by
following pf(u)vs→vk . This strategy could avoid a failed feasibility estimation of a foreseen
path caused by the imbalance problem of SI at vk.
(b): identify the CBLPs based on the BLPs with the maximal SI . To avoid the
120 Finding the Optimal Social Trust Path
Algorithm 16: Forward Search ()Data: MT (vs, vt), AQµ(p
b(δ)vk→vt ), AQµ(p
b(µ)vk→vt ), AQµ(p
CBLP (µ)vk→vt ), µ ∈ {T, SI, CIF}, QT
vs,vt, QSI
vs,vt,
QCIFvs,vt
Result: pforwardvs→vt , F(pforward
vs→vt )begin
Set vy .d = ∞ (vy 6= vs), vs.d = 0, S1y = S2
y = ∅,pf(u)vs→vs = vs;
Add vs into S1y and S2
y ;while S1
y 6= ∅ and S2y 6= ∅ do
v1a.d = min(v∗a.d) (v∗a ∈ S1
y);v2
a.d = min(v2∗a .d) (v2∗
a ∈ S2y);
if v1a = v2
a and v1a.d1 = v2
a.d2 thenfor each vb ∈ adj[v1
a] doif fp
f(u)+b(δ)vs→vb→vt is feasible thenPath Selection(MT (vs, vt), S1
y , v1a, vb);
endelse if fp
f(u)+b(δ)vs→vb→vt is infeasible then
if one of {fpf(u)+b(µ)vs→vj→vt} and {fp
f(u)+CBLP M (µ)vs→vj→vt } is feasible then
Path Selection(MT (vs, vt), S2y , v1
a, vb);end
endend
endelse
for each vb ∈ adj[v1a] do
if fpf(u)+b(δ)vs→vb→vt is feasible thenPath Selection(MT (vs, vt), S1
y , v1a, vb);
endendfor each vb ∈ adj[v2
a] do
if one of {fpf(u)+b(µ)vs→vj→vt , fp
f(u)+CBLP M (µ)vs→vj→vt } is feasible then
Path Selection(MT (vs, vt), S2y , v2
a, vb);end
endendRemove v1
a from S1y and v2
a from S2y ;
endReturn pforward
vs→vt =max utility(pf(u)
vs→v1a→vt
, pf(u)
vs→v2a→vt
) and F(pforwardvs→vt );
end
new imbalance problem of QoT attributes caused by greedily maximizing SI value,
MFPB-HOSTP then identifies M CBLPs at each intermediate node vk, which are com-
posed of pb(SI)vk→vl , l ∈ [1,M ] and p
b(δ)vl→vt , l ∈ [1,M ]. When facing with the new im-
balance problem of QoT attributes caused by maximizing SI value, the identified M
CBLPs at vk are concatenated with the FLP pf(u)vs→vk , to estimate whether there exists a
feasible solution identified by following the FLP. This could help avoid a failed feasi-
bility estimation of a foreseen path caused by the new imbalance problem of the other
two QoT attributes (i.e., T and CIF ) at vk.
§5.6 The Proposed MFPB-HOSTP for Optimal Social Trust Path Selection 121
Step 4 (identify the BLP with the maximal aggregated CIF value and the
corresponding CBLPs):
(a): identify the BLPs with the maximal CIF . To avoid the imbalance problem
of CIF , in this step, at each intermediate node vk, MFPB-HOSTP first identifies the
BLP with the maximal aggregated CIF value (denoted as pb(CIF )vk→vt ) based on the Dijk-
stra’s shortest path algorithm [31]. In this search process, at each vk, the aggregated
QoT attributes values of pb(CIF )vk→vt are computed and recorded. When facing with the
imbalance problem of CIF at vk, BLP pb(CIF )vk→vt is concatenated with the FLP p
f(u)vk→vt ,
forming a new foreseen path fpf(u)+b(CIF )vs→vk→vt . This strategy could help avoid a failed
feasibility estimation of a foreseen path caused by the imbalance problem of CIF at
vk.
(b): identify the CBLPs based on the BLPs with the maximal CIF . To avoid
the new imbalance problems of QoT attributes caused by greedily maximizing CIF
value, MFPB-HOSTP then identifies M CBLPs at each intermediate node vk, which
are composed of pb(CIF )vk→vl , l ∈ [1,M ] and p
b(δ)vl→vt , l ∈ [1,M ]. When facing with the new
imbalance problem of QoT attributes caused by the BLP with the maximal CIF at vk,
the M CBLPs at vk are concatenated with the FLP pf(u)vs→vk , to estimate the feasibility
of searching by following the FLP. This could avoid a failed feasibility estimation of
a foreseen path caused by the new imbalance problem of the other two QoT attributes
(i.e., T and SI) at vk.
In summary, the Backward Search procedure can illustrate whether there exists a
feasible solution in a sub-network. In addition, if a feasible solution exists, compared
with the Backward Search procedure of H OSTP, MFPB-HOSTP identifies the BLP
with the maximal aggregated value of each of the QoT attributes. Furthermore, to
solve a new imbalance problem of QoT attributes caused by greedily maximizing the
aggregated values of QoT attributes, MFPB-HOSTP also identifies several CBLPs,
which are composed of part of the BLP with the minimal δ and part of the BLP with
the maximal aggregated value of each of the QoT attributes. When facing with an
imbalance problem of QoT attributes, the identified BLPs and CBLPs will be used in
122 Finding the Optimal Social Trust Path
the following Forward Search procedure aiming to avoid a failed feasibility estimation
of a foreseen path in H OSTP and deliver a near-optimal solution. Next we discuss
the search strategies adopted in the following Forward Search procedure of MFPB-
HOSTP.
Forward Search: In the forward search from vs to vt, MFPB-HOSTP uses the
BLPs and CBLPs identified by the above Backward Search procedure to investigate
whether there exists another path pforwardvs→vt
, which is better in quality than the above
path pbackwardvs→vt
= pb(δ)vs→vt returned in the Backward Search procedure (i.e., whether
F(pforwardvs→vt
) > F(pbackwardvs→vt
)).
In this procedure, MFPB-HOSTP searches the path with the maximal F value
from vs to vt. Assume node vm ∈ {neighboring nodes of vs} is selected based on
the Dijkstra’s shortest path algorithm (i.e., FLP pf(u)vs→vm is identified). Then, MFPB-
HOSTP concatenates the FLP with BLP pb(δ)vm→vt to form a foreseen path fp
f(u)+b(δ)vs→vm→vt .
If the foreseen path is feasible, MFPB-HOSTP then chooses the next node from vm
with the maximal F value. Otherwise, MFPB-HOSTP concatenates the FLP with
the BLPs with the minimal T , SI and CIF respectively to form three foreseen paths
{fpf(u)+BLP (µ)vs→vm→vt (µ ∈ {T, SI, CIF})}. According to the feasibility of these foreseen
paths, MFPB-HOSTP adopts the following search strategies.
Situation 1: If one of {fpf(u)+b(µ)vs→vm→vt (µ ∈ {T, SI, CIF})} is feasible, MFPB-
HOSTP adopts the following two strategies to identify two social trust paths and se-
lects the feasible social trust path with the higher utility value as the final solution.
1. Strategy 1: MFPB-HOSTP identifies one path by choosing the next node from
vm with the maximal F value.
2. Strategy 2: MFPB-HOSTP identifies another path by searching another neigh-
boring node of vs with the maximal F , which is the same as the search strategy
adopted in H OSTP.
Situation 2: If all {fpf(u)+b(µ)vs→vm→vt µ ∈ {T, SI, CIF}} are infeasible, then at vm,
MFPB-HOSTP concatenates the FLP with the CBLPs to form the foreseen paths
§5.6 The Proposed MFPB-HOSTP for Optimal Social Trust Path Selection 123
(i.e., {fpf(u)+CBLP M (µ)vs→vm→vt ). According to the feasibility of these foreseen paths, MFPB-
HOSTP adopts the following search strategies.
1. Sub-situation 2.1: If one of {fpf(u)+CBLP M (µ)vs→vm→vt is feasible, MFPB-HOSTP iden-
tifies two social trust paths based on Strategies 1 and 2 in the above Situation
1, and selects the feasible social trust path with the higher utility as the final
solution.
2. Sub-situation 2.2: If all of {fpf(u)+CBLP M (µ)vs→vm→vt are infeasible, MFPB-HOSTP
does not search the path from vm. Instead, MFPB-HOSTP performs the For-
ward Search procedure to search the path from vs in the sub-network without
taking link vs → vm into consideration.
Based on the Theorem 2 in H OSTP, we can see that the social trust path pforwardvs→vt
identified by the Forward Search procedure of MFPB-HOSTP can not be worse than
the feasible social trust path pbackwardvs→vt
identified by the Backward Search procedure.
Namely, F(pforwardvs→vt
) ≥ F(pbackwardvs→vt
). In addition, if there exists only one feasible so-
lution in the sub-network, it can be identified by both the Backward Search procedure
and the Forward Seach procedure, and it is the optimal solution. Otherwise, if there
exist more than one feasible solutions in the sub-network, then the solution identified
by the Forward Seach procedure is near-optimal or optimal, which is better than the
one identified by the Backward Search procedure.
5.6.4 Summary
Based on the above discussion, during the Backward Search procedure, MFPB-HOSTP
could illustrate whether there exists a feasible solution in a sub-network (it is proved
by Theorem 1 in H OSTP). If a feasible solution exists, MFPB-HOSTP then iden-
tifies several BLPs and CBLPs at each intermediate node rather than only one BLP
in H OSTP. During the Forward Search procedure, MFPB-HOSTP delivers a near-
optimal solution which is no worse than the one returned by the Backward Search
124 Finding the Optimal Social Trust Path
procedure (it is proved by Theorem 2 in H OSTP). In this search process, the identi-
fied BLPs and CBLPs are used to concatenate with the FLP, forming multiple foreseen
paths rather than one foreseen path only in H OSTP. These foreseen paths could help
avoid a failed feasibility estimation of a foreseen path caused by the imbalance prob-
lem of QoT attributes.
In the Backward Search procedure, in order to identify 4 BLPs for the minimal δ
and the maximal value of each QoT attribute (i.e, T , SI and CIF ), MFPB-HOSTP
adopts the Dijkstra’s shortest path algorithm 4 times with the time complexity of O(4∗(NlogN + E)) [31] (N is the number of nodes and E is the number of links). In
addition, in the worst case, the time complexity of identifying the CBLPs for three
QoT attributes by MFPB-HOSTP is O(3∗(KN)), where K is the maximal path length
in a sub-network. So, the time complexity of the Backward Search procedure is O(4 ∗(NlogN + E) + 3 ∗KN).
In the Forward Search procedure, in the worst case, MFPB-HOSTP adopts the Di-
jkstra’s shortest path algorithm twice with the time complexity of O(2∗(NlogN +E))
[31]. In addition, in the worst case, the time complexity of evaluating the feasi-
bility of foreseen paths is O(KE). So, the time complexity of MFPB-HOSTP is
O(NlogN + KE).
In social networks, following the small-world2 characteristic, it is usually the case
that K ≤ 7 [101]. Therefore, the time complexity of MFPB-HOSTP is O(NlogN +
E), which is the same as that of H OSTP. But our proposed heuristic algorithm has bet-
ter search strategies than H OSTP. Thus MFPB-HOSTP delivers a solution no worse
than that of H OSTP, and as our experiments confirm, MFPB-HOSTP can deliver bet-
ter solutions than H OSTP in some cases.
2The average path length between any two nodes is about 6 hops in a social network.
§5.7 Experiments on MFPB-HOSTP 125
Table 5.7: The setting of QoT constraintsConstraint ID QT
vs,vtQSI
vs,vtQCIF
vs,vt
1 0.01 0.01 0.012 0.05 0.05 0.053 0.1 0.1 0.14 0.15 0.15 0.155 0.2 0.2 0.26 0.25 0.25 0.257 0.3 0.3 0.38 0.35 0.35 0.359 0.4 0.4 0.4
10 0.2 0.05 0.0511 0.05 0.2 0.0512 0.05 0.05 0.213 0.25 0.05 0.0514 0.05 0.25 0.0515 0.05 0.05 0.2516 0.3 0.05 0.0517 0.05 0.3 0.0518 0.05 0.05 0.319 0.35 0.05 0.0520 0.05 0.35 0.0521 0.05 0.05 0.3522 0.4 0.05 0.0523 0.05 0.4 0.0524 0.05 0.05 0.4
5.7 Experiments on MFPB-HOSTP
5.7.1 Experiment Settings
We select the Enron email dataset with 87,474 nodes (participants) and 30,0511 links
(formed by sending and receiving emails) for our experiments. As we analysed in
Chapter 5.4, our proposed H OSTP outperforms prior algorithms in both efficiency
and the quality of identified social trust path. Therefore, in order to study the perfor-
mance of our proposed algorithm, we compare MFPB-HOSTP with H OSTP in both
execution time and the utilities of the identified social trust paths. In our experiments,
since the detailed mining method of QoT attribute values (i.e., T , SI and CIF ) is out
126 Finding the Optimal Social Trust Path
Table 5.8: The setting of the weight of QoT attributesWeight ID wT wSI wCIF
1 0.5 0.25 0.252 0.25 0.5 0.253 0.25 0.25 0.5
Table 5.9: The properties of the simplest and the most complex sub-networks in each group ofhops
HopsThe simplest sub-network The most complex sub-networkID Nodes Links ID Nodes Links
4 1 33 56 20 393 15435 1 49 90 20 680 26706 1 48 74 20 1300 63967 1 40 64 20 964 4955
of the scope of this thesis, and they could have different values in different applica-
tions, the QoT attribute values are randomly generated by using rand() in Matlab.
Source participants may specify different QoT constraints for the social trust path
selection in different domains. In order to investigate the performance of MFPB-
HOSTP with different QoT constraints values, 24 sets of QoT constraints are specified
and listed in Table 5.7, which cover some possible settings of QoT constraints. In some
cases (i.e., constraint IDs 1 to 9), the values of QoT constraints are the same, and in the
rest of the cases (i.e., constraint IDs 10 to 24), the constraint of one QoT attribute (i.e.,
T , SI or CIF ) is larger than the values of the other two QoT attributes. In addition, in
order to investigate the performance of MFPB-HOSTP in path selection with different
weights of the QoT attributes in the utility function, three sets of weights are specified
and listed in Table 5.8, where T , SI and CIF are given a lager weight than other two
QoT attributes respectively.
In order to study the performance of our proposed heuristic algorithm in the sub-
networks of different scales and structures, we first randomly select 80 pairs of source
and target participants from the Enron email dataset1. We then extract the correspond-
ing 80 sub-networks between them by using the exhaustive search method. Among
them, the maximal length of a social trust path varies from 4 to 7 hops following the
§5.7 Experiments on MFPB-HOSTP 127
0
10
20
0
5
10
15
200
0.2
0.4
0.6
0.8
1
QoT constraint IDsub−network ID
utili
ty
0
10
20
0
5
10
15
200
0.2
0.4
0.6
0.8
1
QoT constraint IDsub−network ID
utili
ty
MFPB−HOSTPH_OSTP
S1: infeasible
S3: same
S2: better
S1: infeasibleS3: same
S2: better
4 hops, WID=1 5 hops, WID=1
Figure 5.10: The path utilities of sub-networks with 4 and 5 hops based on WID=1
small-world characteristic. These sub-networks are grouped by the number of hops.
In each group they are ordered by the number of nodes in them. Table 5.9 lists the
properties of the simplest and the most complex sub-networks in each group of hops.
The simplest sub-network has 33 nodes and 56 links (4 hops), while the most complex
sub-network has 1300 nodes and 6396 links (6 hops). With each sub-network, we run
MFPB-HOSTP and H OSTP 3 times independently to calculate the average execution
time.
Both MFPB-HOSTP and H OSTP are implemented using Matlab R2008a running
on an IBM ThinkPad SL500 laptop with an Intel Core 2 Duo T5870 2.00GHz CPU,
3GB RAM, Windows XP SP3 operating system and MySql 5.1.35 database.
5.7.2 Results and Analysis
Results and analysis of path utility. Fig. 5.10 to Fig. 5.15 plot the path utilities of the
identified social trust paths in the sub-networks categorised in groups of hops. From
these figures, we can observe that if there are no feasible solutions in a sub-network,
both of MFPB-HOSTP and H OSTP can investigate the infeasibility (e.g., case S1 in
Fig. 5.10 to Fig. 5.15). This is because both of them perform a backward search
128 Finding the Optimal Social Trust Path
0
10
20
0
5
10
15
200
0.2
0.4
0.6
0.8
1
QoT constraint IDsub−network ID
utili
ty
0
10
20
0
5
10
15
200
0.2
0.4
0.6
0.8
1
QoT constraint IDsub−network ID
utili
ty
MFPB−HOSTPH_OSTP
S2: better
S1: infeasible
S3: same
S1: infeasibleS2: better
S3: same
5 hops, WID=24 hops, WID=2
Figure 5.11: The path utilities of sub-networks with 4 and 5 hops based on WID=2
0
10
20
0
5
10
15
200
0.2
0.4
0.6
0.8
1
QoT constraint IDsub−network ID
utilt
iy
0
10
20
0
5
10
15
200
0.2
0.4
0.6
0.8
1
QoT constraint IDsub−network ID
utili
ty
MFPB−HOSTPH_OSTP
S2: better
S3: same
S1: infeasible S1: infeasible
S3: same
S2: better
4 hops, WID=3 5 hops, WID=3
Figure 5.12: The path utilities of sub-networks with 4 and 5 hops based on WID=3
§5.7 Experiments on MFPB-HOSTP 129
0
10
20
0
5
10
15
200
0.2
0.4
0.6
0.8
1
QoT constraint IDsub−network ID
utili
ty
0
10
20
0
5
10
15
200
0.2
0.4
0.6
0.8
1
QoT constraint IDsub−network ID
utili
ty
MFPB−HOSTPH_OSTP
S3: sameS2: better
S1: infeasible S1: infeasible
S3: same
6 hops, WID=1 7 hops, WID=1
Figure 5.13: The path utilities of sub-networks with 6 and 7 hops based on WID=1
from vt to vs to identify the social trust path with the minimal δ. It has been proved
in Theorem 1 that this procedure can always investigate whether there exists a feasible
solution in a sub-network.
From Fig. 5.10 to Fig. 5.15, we can see that in all cases of the 80 sub-networks,
our MFPB-HOSTP does not yield any feasible social trust path with a utility worse
than that of H OSTP (e.g., cases S2 and S3 in Fig. 5.10 to Fig. 5.15). This is because
in the Forward Search procedure, if there is no imbalance problem of QoT attributes,
MFPB-HOSTP identifies the same social trust path with H OSTP. When facing with
an imbalance problem of QoT attributes, MFPB-HOSTP identifies two social trust
paths, out of which one path is identified by using the same search strategy adopted in
H OSTP (see Strategy 2 of Situation 1 in Section 5.6.3), and selects the feasible path
with the higher utility as the solution. Therefore, MFPB-HOSTP does not yield any
solution worse than that of H OSTP in any cases.
According to our experimental results, in 27 out of 75 sub-networks with feasi-
ble solutions (i.e., 36% of total sub-networks with feasible solutions), MFPB-HOSTP
can deliver better social trust paths than H OSTP (e.g., case S2 in Fig. 5.10 to Fig.
5.15). The sums of utilities computed by MFPB-HOSTP and H OSTP in these sub-
130 Finding the Optimal Social Trust Path
0
10
20
0
5
10
15
200
0.2
0.4
0.6
0.8
1
QoT constraint IDsub−network ID
utili
ty
0
10
20
0
5
10
15
200
0.2
0.4
0.6
0.8
1
QoT constraint IDsub−network ID
utili
ty
MFPB−HOSTPH_OSTP
S1: infeasible
S3: sameS2: betterS3: same
S1: infeasible
S2: better
6 hops, WID=2 7 hops, WID=2
Figure 5.14: The path utilities of sub-networks with 6 and 7 hops based on WID=2
0
10
20
0
5
10
15
200
0.2
0.4
0.6
0.8
1
QoT constraint IDsub−network ID
utili
ty
0
10
20
0
5
10
15
200
0.2
0.4
0.6
0.8
1
QoT constraint IDsub−network ID
utili
ty
MFPB−HOSTPH_OSTP
S2: better
S1: infeasible S3: same
S2: better
S1: infeasibleS3: same
6 hops, WID=3 7 hops, WID=3
Figure 5.15: The path utilities of sub-networks with 6 and 7 hops based on WID=3
§5.7 Experiments on MFPB-HOSTP 131
networks with each group of hops are listed in Table 5.10, where we can see that the
sum of utilities of our proposed MFPB-HOSTP algorithm is 15.94% more than that of
H OSTP in 4 hops sub-networks, 46.51% more in 5 hops, 12.63% more in 6 hops and
17.79% more in 7 hops. This is because when facing with an imbalance problem of
QoT attributes at an intermediate node vk, in addition to pb(δ)vk→vt , more BLPs are con-
catenated with the FLP identified by the forward search procedure, forming multiple
foreseen paths and helping avoid a failed feasibility estimation. Thus MFPB-HOSTP
can deliver a better solution than H OSTP in some cases.
Table 5.10: The comparison of path utilityAlgorithms The sum of path utility (sec)
4 hops 5 hops 6 hops 7 hops totalMFPB-HOSTP 11.7634 11.2517 6.3161 2.1140 31.4452
H OSTP 10.1459 7.6797 5.6076 1.7947 25.2279difference 15.94%more 46.51%more 12.63%more 17.79%more 24.64%more
Results and analysis of the execution time.
Fig. 5.16 to Fig. 5.17 plot the average execution time of the social trust path se-
lection with three different weights of QoT attributes. From these figures we can see
that in most cases (i.e., 3082/5760=53.5% of total cases), MFPB-HOSTP has the same
execution time as that of H OSTP (e.g., case S4 in Fig. 5.16 to Fig. 5.17). This is be-
cause if no feasible solution exists in the sub-network, based on Theorem 1 in H OSTP,
both of MFPB-HOSTP and H OSTP can identify this and stop the search process, re-
sulting in the same execution time. In addition, in the rest of the cases, MFPB-HOSTP
consumes more execution time than H OSTP (e.g., case S5 in Fig. 5.16 to Fig. 5.17).
This is because if a feasible solution exists in a sub-network, at each intermediate node
vk, in addition to pb(δ)vs→vk , MFPB-HOSTP identifies multiple BLPs (i.e., the BLPs with
the maximal aggregated value of each of QoT attribute and M CBLPs for each QoT
attribute) in the Backward Search procedure, rather than one BLP only in H OSTP
(see Section 5.6.3). Moreover, when facing with the imbalance problem of QoT at-
tributes at vk, MFPB-HOSTP needs to identify two social trust paths. The total exe-
cution time of each of MFPB-HOSTP and H OSTP in sub-networks with each group
of hops is listed in Table 5.11, where we conclude that the difference of the execution
132 Finding the Optimal Social Trust Path
0
10
20
0
5
10
15
200
5
10
15
QoT constraint IDsub−network ID
exec
utio
n tim
e (s
ec)
0
10
20
0
5
10
15
200
10
20
30
40
50
60
QoT constraint IDsub−network ID
exec
utio
n tim
e (s
ec)
MFPB−HOSTPH_OSTP
5 hops4 hops
S4: sameS4: same
S5: more timeS5: more time
Figure 5.16: The execution time of sub-networks with 4 and 5 hops
time between MFPB-HOSTP and H OSTP is similar in sub-networks with each group
of hops. On average, the execution time of MFPB-HOSTP is 1.288 times of that of
H OSTP.
Through the above experiments conducted on the sub-networks with different scales
and structures, we can see that on average MFPB-HOSTP consumes 1.288 times of the
execution time of H OSTP while delivering better solutions in sub-networks. Since
MFPB-HOSTP has the same polynomial time complexity (i.e, O(NlogN + E)) as
H OSTP, MFPB-HOSTP is superior to H OSTP when applied to large-scale social
networks.
Table 5.11: The comparison of execution timeAlgorithms The sum of execution time (sec)
4 hops 5 hops 6 hops 7 hops totalMFPB-HOSTP 7.6478e+003 2.3537e+004 2.5621e+004 4.2355e+004 9.9161e+004
H OSTP 5.7831e+003 1.8529e+004 1.9903e+004 3.2776e+004 7.6991e+004difference 1.3224:1 1.2703:1 1.2873:1 1.2922:1 1.2880:1
§5.8 Conclusion 133
0
10
20
0
5
10
15
200
10
20
30
40
50
QoT constraint IDsub−network ID
exec
utio
n tim
e (s
ec)
0
10
20
0
5
10
15
200
20
40
60
80
100
QoT constraint IDsub−network ID
exec
utio
n tim
e (s
ec)
MFPB−HOSTPH_OSTP
6 hops7 hops
S5: more timeS4: same S5: more time
S4: same
Figure 5.17: The execution time of sub-networks with 6 and 7 hops
5.8 Conclusion
In this Chapter, we have proposed a general concept QoT (Quality of Trust), and mod-
elled the QoT constrained optimal social trust path selection as the classical Multiple
Constrained Optimal Path (MCOP) problem, which is NP-Complete [67]. For solving
the NP-Complete optimal social trust path selection problem, we have proposed an ap-
proximation algorithm, called MONTE K, by adopting the Monte Carlo method and
our proposed optimization strategies. In addition, we have proposed a heuristic algo-
rithm, called H OSTP based on the Dijkstra’s shortest path algorithm and our proposed
optimization strategies. Furthermore, to address the drawbacks included in H OSTP
(i.e., the imbalance problem of QoT attributes), we have proposed a heuristic algo-
rithm, called MFPB-HOSTP, an efficient heuristic algorithm, where multiple foreseen
paths are formed, helping avoid a failed feasibility estimation of a foreseen path caused
by the imbalance problem of QoT attributes. The results of experiments conducted on
real social network datasets demonstrate that the proposed methods outperform the
existing methods in optimal social trust path selection with good efficiency.
The trust path selection methods proposed in this chapter can select the most trust-
134 Finding the Optimal Social Trust Path
worthy social trust path to efficiently and effectively deliver reasonable propagated
trust values between two unknown participants, which is significant and essential in
the trust management of OSNs. In social network based real applications, the pro-
posed methods can for instance help a buyer to find the most trustworthy seller who
sells the products preferred by the buyer, or help an employer to find the most trust-
worthy potential employees.
Chapter 6
Finding K Optimal Social Trust Paths
In Chapter 5, we have introduced the proposed optimal social trust path algorithms.
But these studies focus on selecting only one social trust path between a source par-
ticipant and a target participant. As illustrated in cognitive science [68], people are
willing to believe what they have been told most often and by the possibility of the
greatest number of different sources. Therefore, in order to obtain a more reasonable
trust evaluation result of a target participant, a source participant may refer to multiple
social trust paths from the source participant to the target one. This requires identifying
K (K ≥ 2) optimal social trust paths, yielding the K most trustworthy trust propa-
gation results based on the constraints specified by the source participant. Since the
selection of any one of the K optimal social trust paths based on multiple constrains
is the classical MCOP selection problem, which has been proved to be NP-Complete
[67], the Multiple Constrained K Optimal Social Trust Paths (MCOP-K) selection is
also an NP-Complete problem. But the existing algorithms [33, 94, 100] for K paths
selection attempt to find the K shortest paths without any end-to-end constrains, and
this is not an NP-Complete problem. Thus, they cannot be used for the MCOP-K
selection problem.
In this chapter, in order to solve the NP-Complete MCOP-K selection problem in
complex trust-oriented social networks, we propose a new efficient Heuristic algorithm
for the K Optimal Social Trust Path selection based on the Dijkstra’s shortest path
algorithm [31] and our optimization strategies, called H-OSTP-K. In addition, we have
conducted extensive experiments on a real online social network dataset, the Enron
135
136 Finding K Optimal Social Trust Paths
email dataset. Experimental results demonstrate that H-OSTP-K outperforms existing
methods in the quality of identified social trust paths and the efficiency.
6.1 K Optimal Social Trust Paths Selection
In this section, we first analyse some existing algorithms for K shortest paths selection
and then propose an efficient heuristic algorithm H-OSTP-K for the NP-Complete
MCOP-K selection in complex social networks.
6.2 Existing Algorithms
K shortest paths selection has been used in many applications, such as power transmis-
sion route selection, automatic translation between natural languages, and biological
sequence alignment [33]. In the literature, several algorithms have been proposed to
solve the K shortest paths selection problem, including (1) algorithms to find K gen-
eral shortest path (paths allowing loops), and (2) algorithms to find K simple shortest
paths (paths without loops) [33]. As a social trust path may contain loops [48], we
introduce some existing algorithms for finding K general shortest paths as follows.
The algorithms for finding K general shortest paths can be classified into two cat-
egories. They are (1) K general paths selection based on the Dijkstra’s shortest algo-
rithm [31], and (2) K general paths selection based on A∗ algorithm.
6.2.1 Category 1
In Category 1, Fox [39] proposed a K paths selection algorithm, where each interme-
diate node vk, (vk 6= vs) records up to K minimal path lengths from vs to vk. At each
step, up to K nodes are selected from a priority queue as the expansion nodes based on
the maximal path length record at the nodes. If a node is selected, the algorithm counts
the number of times it has been visited. If all the nodes have been visited K times,
the K shortest paths from vs to each node of the sub-network are selected. Miaou
§6.2 Existing Algorithms 137
[100] proposed a similar algorithm by using a binary heap to store the priority queue,
which improves the efficiency of K path selection. The time complexity of this type
of algorithm is O(m + Knlogn). Throughout this chapter, K (K ≥ 2) stands for the
number of selected paths, m for the number of links, and n for the number of nodes.
6.2.2 Category 2
In Category 2, Yen proposed a classic K general shortest paths selection algorithm
based on the A∗ algorithm [133]. This algorithm first computes the shortest path from
vs to vt. Then it regards each node of the newly discovered shortest path as a deviation
node. For each deviation node, this algorithm executes a single-source shortest path
algorithm from the deviation node to vt, forming a candidate deviation path. The next
shortest path is chosen from all the candidates deviation paths with the minimal path
length. This process continues until K different shortest paths are finally determined.
In addition, Martins [94] improved the runtime performance of Yen’s algorithm by or-
dering the deviation node based on deviation paths’ length. Furthermore, Eppsten [33]
proposed a well-known K general shortest paths selection algorithm. This algorithm
builds a shortest path tree rooted at the target node first, and then selects certain links
outside the shortest path tree, forming the paths to be discovered. The time complexity
of Eppsten’s algorithm reaches O(m + nlogn + K), which is also the lowest bound of
the K general paths selection problem.
The above algorithms address the K general shortest path selection problem well.
However, they are all deterministic and thus cannot be used to solve the NP-Complete
MCOP-K selection problem [6].
138 Finding K Optimal Social Trust Paths
6.3 The Proposed H-OSTP-K for K Optimal Social Trust
Paths Selection
In this section, we propose a novel heuristic algorithm H-OSTP-K, for the K optimal
social trust path selection with end-to-end QoT constraints in complex social networks.
In H-OSTP-K, we first adopt the Backward K-Search procedure from vt to vs to (1)
investigate whether there exists a feasible solution in the sub-network, (2) indicate the
number of feasible solutions when this number is less than K (K ≥ 2), and (3) record
the aggregated QoT attributes (i.e., T, SI and CIF ) of the identified K paths from
vt to each intermediate node vk. If there exists at least one feasible solution, we then
adopt the Forward K-Search procedure to search the network from vs to vt to deliver
up to K near-optimal solutions with the K best utilities (the utility function has been
defined in Section 5.1.3).
In MOCP-K selection, if a path satisfies multiple QoT constraints, it means that
each aggregated QoT attribute of that path should be larger than the corresponding
QoT constraint. Based on this observation, we adopt the objective function proposed in
Section 5.4.1 ( Eq. (5.7)) to investigate whether the aggregated QoT attributes of a path
can satisfy the QoT constraints, where δ(p) ≤ 1, if and only if each aggregated QoT
attribute of a social trust path satisfies the corresponding QoT constraint. Otherwise
δ(p) > 1.
6.3.1 Algorithm Description of H-OSTP-K
Backward K-Search: Assume there exist at least K social trust paths in the sub-
network. In the backward search from vt to vs, H-OSTP-K identifies K social trust
paths from vt to vs (denoted as pB1vs→vt
to pBKvs→vt
) with the K minimal δ based on the
Dijkstra’s shortest path algorithm [31]. In the searching process, at vk, the aggregated
QoT attributes of K paths from vt to vk with the K minimal δ are recorded. According
to the Theorem 1 proposed in Section 5.4.1, the Backward K-Search procedure can
§6.3 The Proposed H-OSTP-K for K Optimal Social Trust Paths Selection 139
investigate whether there exists a feasible solution in the sub-network. In addition,
according to Theorem 3 given below, this procedure can also indicate the number of
feasible solutions when there exist less than K feasible solutions in the sub-network
(see Algorithm 18).
Theorem 3: In the Backward K-Search procedure, the process of identifying K paths
with the K minimal δ can indicate the number of feasible solutions when there exist
less than K feasible solutions in a sub-network.
Proof: Let pB1vs→vt
, ..., pBKvs→vt
be the K paths identified by the Backward Search
procedure from vt to vs with the K minimal δ value, and S is the number of feasible
solutions in the subnetwork between vs and vt. In the identified K paths from vs
to vt, if there exists G (0 < G < K) paths (denoted as pB1vs→vt
, ..., pBGvs→vt
), where
δ(pB1vs→vt
) ≤ 1, ..., δ(pBGvs→vt
) ≤ 1, then based the theorems in proposed in Section
5.4.1, there exist at least G feasible solutions in the sub-network between vs and vt
(i.e., S ≥ G). In addition, the Backward Search procedure can always identify K
paths with K minimal δ value [100]. Therefore, there exist no more than G feasible
solutions in the sub-network between vs to vt (i.e., S ≤ G). Then S = G. 2
Without loss of generality, we assume there are at least K social trust paths in the
sub-network, though not all of them are feasible solutions. The Backward K-Search
can always identify K paths with the K minimal δ. In all the identified K paths, if
δmin > 1, it indicates there is no feasible solution in the sub-network. If δmin ≤ 1, it
indicates there exists at least one feasible solution. In addition, if there exist G (0 <
G < K) paths, where the δ values of these paths are no more than one, it means there
are G feasible solutions in the sub-network.
Forward K-Search: Assume there exist at least K (K ≥ 2) feasible solutions
in the sub-network. In the Forward K-Search procedure, the aggregated QoT at-
tribute values recorded at each vk is adopted to identify whether there exist further
K paths pF1vs→vt
, ..., pFKvs→vt
, each of which is better than the corresponding path of
pB1vs→vt
, ..., pBKvs→vt
(i.e.,F(pF1vs→vt
) > F(pB1vs→vt
), ...,F(pFKvs→vt
) > F(pBKvs→vt
) (see Al-
gorithm 19).
140 Finding K Optimal Social Trust Paths
Algorithm 17: H-OSTP-KData: M , QT
vs,vt, QSI
vs,vt, QCIF
vs,vt, vs, vt, K
/* M is an adjacency matrix thatrepresents the sub-network between vs and vt */Result: F(pF1
vs→vt )...F(pFGvs→vt )
1 begin2 ps = ∅, pt = ∅;3 Backward K-Search (M , QT
vs,vt, QSI
vs,vt, QCIF
vs,vt, vs, vt, K);
4 if Min δ(pB1vs→vt )...δ(p
BKvs→vt ) > 1 then
5 return no feasible solution;end
6 else7 return G,BAQoT (v).T , BAQoT (v).SI , BAQoT (v).CIF ;
/* G is the number of feasible solution identified by the Backward K-Search procedure, and BAQoT recordsthe aggregated QoT attributes in the backward search. */
8 Forward K-Search (M , BAQoT (v).T , BAQoT (v).SI , BAQoT (v).CIF , QTvs,vt
, QSIvs,vt
, QCIFvs,vt
,vs, vt, G);
9 Return F(pF1vs→vt ), ...,F(p
FGvs→vt );
endend
In this procedure, H-OSTP-K first searches the path with the K maximal F value
from vs. Assume node vm ∈ {neighboring nodes of vs} is selected based on the
Dijkstra’s shortest path algorithm in the ith path (i ∈ [1, K]). H-OSTP-K calculates
the aggregated QoT attribute values of the path from vs to vm (denoted as path pFivs→vm
).
Then K foreseen paths from vs to vt via vm (denoted as fpFi+Bσvs→vm→vt
= pFivs→vm
+
pBσvm→vt
(σ ∈ [1, K])) are formed. Depending on whether fpFi+Bσvs→vm→vt
is feasible, H-
OSTP-K adopts the following searching strategies.
Situation 1: If each aggregated QoT attribute of one of the foreseen paths from
vs to vt via vm, (i.e., fpFi+Bσvs→vm→vt
(σ ∈ [1, K]) satisfies the corresponding end-to-end
QoT constraint, then vm is put into the priority queue for the next search step.
Situation 2: If all the foreseen paths fpFi+Bσvs→vm→vt
(σ ∈ [1, K]) are infeasible, vm
is not put into the priority queue. Subsequently, H-OSTP-K performs the Forward K-
Search procedure to search the path from vs in the sub-network without taking the link
vs → vm into consideration.
Theorem 4: If vt is selected from the priority queue, then a social trust path from vs
to vt is identified (denoted as pt). If any of the K optimal social trust paths has not
been identified, pt is one of the K optimal social trust paths.
§6.3 The Proposed H-OSTP-K for K Optimal Social Trust Paths Selection 141
Algorithm 18: Backward K-SearchData: M , QT
vs,vt, QSI
vs,vt, QCIF
vs,vt, vs, vt, K
Result: BAQoT (v).T , BAQoT (v).SI , BAQoT (v).CIF1 begin2 set vx.δ = ∞ (vx 6= vt), vt.δ = 0, Sx = ∅, vx.bvisit = 0, G = 0;3 add vt into Sx;4 while Sx 6= ∅ do5 STopK = K min(v∗a.δ) (v∗a ∈ Sx);
/* Sx is the priority queue in the backward search, and STopK is a set that contains the K minimal δ
values. */;6 for each va ∈ STopK do7 if va == vs and va.δ ≤ 1 then8 G = G + 1;
end9 for each vb ∈ adj[va] do
/* adj[va] are all neighboring nodes of va */10 pb = vb to vt via va;11 if vb /∈ Sx then12 put vb into Sx;
end13 else if δ(pb) < max(vb.δ) then14 update BAQoT (vb).T , BAQoT (vb).SI , BAQoT (vb).CIF ;15 put vb into Sx;
endend
16 va.bvisit = va.bvisit + 1;/* the visited times of va plus one */
17 if va.bstatus == K then18 remove va from Sx;
endend
end19 Return G, BAQoT (v).T , BAQoT (v).SI , BAQoT (v).CIF ;
end
Proof: Let pF∗vs→vt
denote the path from vs to vt that is selected from the prior-
ity queue at the J th step. Let pF1vs→vt
, ..., pFKvs→vt
denote the K optimal social trust paths
from vs to vt identified by the Forward K-Search procedure. If pF∗vs→vt
/∈ {pF1vs→vt
, ..., pFKvs→vt
},
then F(pF∗vs→vt
) is less than any of {F(pF1vs→vt
), ...,F(pFKvs→vt
)}. At the J th step, in ad-
dition to vt, there are K − 1 nodes selected from the priority queue. Thus, at least
one node in paths {pF1vs→vt
, ..., pFKvs→vt
} is not selected at the J th step. Then F(pF∗vs→vt
)
is greater than one of {F(pF1vs→vt
), ...,F(pFKvs→vt
)}, which contradicts that F(pF∗vs→vt
) is
less than any of {F(pF1vs→vt
), ...,F(pFKvs→vt
)}. Therefore, Theorem 4 is correct. 2
From Theorem 3 and Theorem 4, H-OSTP-K can identify the number of solutions
when there is less than K solutions, and the first K identified paths by H-OSTP-K are
the top K paths. Based on these properties, we propose two optimization strategies to
improve the efficiency of the Forward K-Search procedure.
142 Finding K Optimal Social Trust Paths
Algorithm 19: Forward K-SearchData: M , BAQoT (v).T , BAQoT (v).SI , BAQoT (v).CIF , QT
vs,vt, QSI
vs,vt, QCIF
vs,vt, vs, vt, G
Result: F(pF1vs→vt ), ...,F(p
FGvs→vt )
1 begin2 set F ′ = 1/F , vy .F ′ = ∞ (vy 6= vs), vs.F ′ = 0, Sy = ∅, vy .fvisit = 0;3 add vs into Sy ;4 J = G;
/* J is the number of unidentified paths from vs to vt. */5 while Sy 6= ∅ do6 STopJ (F ′) = K min(v∗i .F ′) (v∗i ∈ Sy);
/* Sy is the priority queue in the forward search, and STopJ is a set that contains the J minimal F ′ values.*/
7 for each vi ∈ STopJ (F ′) do8 if vi == vt and va.δ ≤ 1 then9 J = J − 1;
/* Only J − 1 paths need to be identified in the following search. */end
10 for each vj ∈ adj[vi] do/* adj[vi] are all neighboring nodes of vi */
11 pj = vs to vj via vi;
12 if ∃fpFi+Bjvs→vj→vt (i, j ∈ [1, G]) is feasible then
13 if vj /∈ Sy then14 put vj into Sy ;
end15 else if F ′(pj) < Max(vj .F ′) then16 update FAQoT (vb).T , FAQoT (vb).SI , FAQoT (vb).CIF ;
/* FAQoT records the aggregated QoT attributes in the forward search. */17 put vj into Sy ;
endend
end18 vi.fvisit = vi.fvisit + 1;
/* the visited times of vi plus one */19 if vi.fvisit == K∗ then20 remove vi from Sx;
endend
end21 Return F(pF1
vs→vt ), ...,F(pFGvs→vt );
end
Optimization Strategy 1: The Forward K-Search procedure is to identify up to
K optimal social trust paths which are feasible. if there exist G (0 < G < K) feasible
solutions identified by the Backward K-Search procedure based on Theorem 1 in a
sub-network, the Forward K-Search procedure does not need to search K paths but G
paths from vs to vt.
Optimization Strategy 2: If vt has been selected J (1 ≤ J < K) times from
the priority queue, in the following process, H-OSTP-K only needs to search K − J
optimal social trust paths from vs to vt.
§6.4 Experiments on H-OSTP-K 143
Then, if there exist l (1 ≤ l ≤ K) feasible solutions, the Forward K-Search pro-
cedure can identify them all, and they are the l optimal social trust paths. Otherwise,
this procedure can identify K feasible solutions which are not worse than those iden-
tified by the Backward K-Search procedure. Namely, Theorem 1 and Theorem 2 can
guarantee the effectiveness of our algorithm.
Since H-OSTP-K adopts the Dijkstra’s shortest path algorithm based K general
social trust paths selection method twice, it has the same time complexity of O(m +
Knlogn) as that of the algorithms in Category 1.
6.4 Experiments on H-OSTP-K
6.4.1 Experiment Settings
To validate our proposed algorithm, we select the Enron email dataset with 87,474
nodes (participants) and 30,0511 links (formed by sending and receiving emails) as
the dataset for our experiments. Firstly, in order to study the performance of our
proposed heuristic algorithm in sub-networks of different scales and structures, we
first randomly select 100 pairs of source and target participants from the Enron email
dataset. We then extract the corresponding 100 sub-networks between them by using
the exhaustive search method. Among them, the maximal length of a social trust path
varies from 4 to 7 hops following the small-world characteristic. These sub-networks
are grouped by the number of hops. In each group they are ordered by the number
of nodes in them. In the simplest case, the sub-network has 33 nodes and 56 links (4
hops), while in the most complex case, the sub-network has 1695 nodes and 11175
links (7 hops).
Secondly, as we have analysed in Section 6.2, existing K general shortest paths
selection algorithms are all deterministic algorithms, and cannot be used for solving
the NP-Complete MCOP-K problem [6]. Therefore, to study the performance of our
heuristic H-OSTP-K, we first compare the maximal utility of the identified K social
144 Finding K Optimal Social Trust Paths
Table 6.1: The setting of QoT constraintsConstraint ID QT
vs,vtQSI
vs,vtQCIF
vs,vt
#1 0.05 0.05 0.05#2 0.1 0.05 0.05#3 0.05 0.1 0.05#4 0.05 0.05 0.1
trust paths with that of our previously proposed H OSTP, which so far outperforms
the other existing algorithms for the NP-Complete Multiple Constrained Optimal so-
cial trust Path (MCOP) selection problem in complex contextual trust-oriented social
networks. In addition, since existing methods are not suitable for the NP-Complete
MCOP-K selection problem, in order to study the efficiency of our proposed opti-
mization strategies, we compare the execution time of H-OSTP-K with that of the
modified version of H-OSTP-K without our proposed optimization strategies (denoted
as H-WOP-K) (see Section 6.4.2).
Finally, to investigate the performance of H-OSTP-K in social trust path selection
with different QoT constraints, four groups of QoT constraints are set and listed in
Table 6.1. In addition, the three QoT attributes are given the same weights in the utility
function. Furthermore, since the detailed mining method of QoT attributes values are
out of scope of this thesis, these QoT attributes values are randomly generated by using
rand() in Matlab.
Each of H-OSTP-K, H-WOP-K and H OSTP is implemented using Matlab R2008a
running on an IBM ThinkPad SL500 laptop with an Intel Core 2 Duo T5870 2.00GHz
CPU, 3GB RAM, Windows XP SP3 operating system and MySql 5.1.35 database.
The results are plotted in Fig. 6.1 to Fig. 6.6, where the execution time of each of
H-OSTP-K and H-WOP-K is averaged based on 3 independent executions.
6.4.2 Results and Analysis
Comparison of Path Utility: Fig. 6.1 plots the path utilities of the identified social
trust path by H OSTP and the maximal path utility of the identified K(K = 2) optimal
§6.4 Experiments on H-OSTP-K 145
12
34
0
10
20
0
0.2
0.4
0.6
QoT constraint IDsub−network ID (4 hops)
utili
ty
12
34
0
10
20
0
0.2
0.4
0.6
QoT constraint IDsub−network ID (5 hops)
utili
ty
12
34
0
10
20
0
0.2
0.4
0.6
QoT constraint IDsub−network ID (6 hops)
utili
ty
12
34
0
10
20
0
0.2
0.4
0.6
QoT constraint IDsub−network ID (7 hops)
utili
ty
H_OSTPH−OSTP−K
S1: infeasible
S3: same
S1: infeasible
S2: better
S2: better
S3: same
S1: infeasible S1: infeasible
S3: sameS3: same
S2: better
Figure 6.1: The path utilities of sub-networks with each group of hops
social trust paths by H-OSTP-K in sub-networks in 4 groups. From these figures, we
can observe that in some sub-networks (i.e., 32 out of 100 sub-networks), if there is no
feasible solution, both H-OSTP-K and H OSTP can investigate the infeasibility (e.g.,
S1 in Fig. 6.1), and thus the path utilities in these sub-networks are zero. This is
because that H OSTP also computes δmin in the backward search from vt to vs based
on the Dijkstra’s shortest path algorithm. Therefore, based on the theorems proposed
in Chapter 5.4, both of them can always investigate whether there is a feasible solution
existing in a sub-network.
In addition, from Fig. 6.1, we can see that in some cases (i.e., 49 out of 100 sub-
networks), H-OSTP-K can deliver the same path utilities with those of H OSTP (e.g.,
S3 in Fig. 6.1). This is because that firstly, in a sub-network, if the path with the
146 Finding K Optimal Social Trust Paths
23
45
1
2
3
4
0
1
2
3
4
5
K
QoT constraint ID
the
sum
of u
tility
K=2K=3K=4K=5
Figure 6.2: The sum of path utilities with different K values
maximal path utility in the K paths identified by H-OSTP-K and the path identified by
H OSTP are selected based on the same foreseen path formed at each of the interme-
diate nodes of these paths, according to the searching strategies in H OSTP proposed
in Chapter 5.4, the two paths are the same. Secondly in a sub-network, if there exists
only one feasible solution, both H-OSTP-K and H OSTP can identify it, and thus they
deliver the same path utility.
Furthermore, from Fig. 6.1, we can also see that H-OSTP-K can deliver better
social trust paths than H OSTP (e.g., S2 in Fig. 6.1) in some cases (i.e., 19 out of 100
sub-networks). In addition, as depicted in Fig. 6.2, given the same constraint ID, the
larger the K value, the greater the sum of the utility of these sub-networks. Table 6.2
lists the sum of utilities computed by H-OSTP-K and H OSTP in these sub-networks,
where we can see that the sum of utilities computed by our proposed heuristic algo-
rithm is 49.66% higher than that of H OSTP in 4 hops sub-networks, 20.24% higher in
5 hops, 13.39% higher in 6 hops. On average, the path utility computed by H-OSTP-K
is 20.29% higher than that of H OSTP. This is because that in H-OSTP-K, it is to form
K foreseen paths rather than only one foreseen path in H OSTP, and thus H-OSTP-K
§6.4 Experiments on H-OSTP-K 147
12
34
0
10
20
0
5
10
QoT constraint IDsub−network ID(4 hops)
exec
utio
n tim
e (s
ec)
12
34
0
10
20
0
10
20
QoT constraint IDsub−network ID(5 hops)
exec
utio
n tim
e (s
ec)
12
34
0
10
20
0
20
40
60
QoT constraint IDsub−network ID(6 hops)
exec
utio
n tim
e (s
ec)
12
34
0
10
20
0
50
100
QoT constraint IDsub−network ID(7 hops)
exec
utio
n tim
e (s
ec)
H−WOP−KH−OSTP−K
S4: same
S4: same
S4: same
S4: same
S5: faster S5: faster
S5: faster S5: faster
Figure 6.3: The execution time of K = 2
148 Finding K Optimal Social Trust Paths
12
34
0
10
20
0
5
10
QoT constraint IDsub−network ID (4 hops)
exec
utio
n tim
e (s
ec)
12
34
0
10
20
0
10
20
30
QoT constraint IDsub−network ID (5 hops)
exec
utio
n tim
e (s
ec)
12
34
0
10
20
0
20
40
60
QoT constraint IDsub−network ID (6 hops)
exec
utio
n tim
e (s
ec)
12
34
0
10
20
0
100
200
300
QoT constraint IDsub−network ID (7 hops)
exec
utio
n tim
e (s
ec)
H−WOP−KH−OSTP−K
S4: sameS4: same
S4: sameS4: same
S5: faster S5: faster
S5: fasterS5: faster
Figure 6.4: The execution time of K = 3
§6.4 Experiments on H-OSTP-K 149
Table 6.2: The comparison of path utility
AlgorithmsThe sum of utility
4 hops 5 hops 6 hops 7 hops totalH-OSTP-K 2.5461 17.9369 8.0839 0 28.5669
H OSTP 1.7012 14.9174 7.1295 0 23.7481difference 49.66% higher 20.24% higher 13.39% higher 0 20.29% higher
have more chances to deliver a better social trust path.
Comparison of Execution Time:
Since H-WOP-K has the same functionality as H-OSTP-K, they both deliver the
same path utilities of K paths in a sub-network. Therefore, we only compare the
difference in their execution time, and the experiment results are plotted in Fig. 6.3 to
Fig. 6.6.
From Fig. 6.3 to Fig. 6.6, we can observe that the execution time of H-OSTP-K
is the same as that of H-WOP-K in some sub-networks (e.g., S4 in Fig. 6.3 to Fig.
6.6). This is because if there is no feasible solution in a sub-network, H-OSTP-K only
performs the Backward K-Search procedure which has the same search strategy with
H-WOP-K. Therefore, they have the same execution time.
In addition, from these figures, we can also observe that the execution time of H-
OSTP-K is less than that of H-WOP-K in other sub-networks (e.g., S5 in Fig. 6.3
to Fig. 6.6). The total execution time of each of H-OSTP-K and H-WOP-K in each
group of hops is listed in Table 6.3, where we can see that the total execution time of
our proposed heuristic algorithm is only 41.86% of that of H-WOP-K in 4 hops sub-
networks, 70.60% in 5 hops, 89.51% in 6 hops and 51.03% in 7 hops. On average,
H-OSTP-K is 37.22% faster than H-WOP-K. From the above results, we can see that
H-OSTP-K is much more efficient than H-WOP-K. The reasons are twofold. Firstly
based on Theorem 3, if there exist G (0 < G < K) feasible solutions, then H-OSTP-K
searches only G optimal social trust paths from vs to vt, significantly saving execution
time (see details in Optimization Strategy 1). Secondly, based on Theorem 4, assuming
there exist K (K ≥ 2) feasible solutions and vt has been selected J (0 < J <
150 Finding K Optimal Social Trust Paths
12
34
0
10
20
0
5
10
QoT constraint IDsub−network ID(4 hops)
exec
utio
n tim
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ec)
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exec
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ec)
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exec
utio
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QoT constraint IDsub−network ID(7 hops)
exec
utio
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e (s
ec)
H−WOP−KH−OSTP−K
S4: same
S4: same
S4: same
S4: same
S5: faster S5: faster
S5: fasterS5: faster
Figure 6.5: The execution time of K = 4
§6.4 Experiments on H-OSTP-K 151
12
34
0
10
20
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QoT constraint IDsub−network ID(4 hops)
exec
utio
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e (s
ec)
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exec
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ec)
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QoT constraint IDsub−network ID(6 hops)
exec
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200
400
600
QoT constraint IDsub−network ID(7 hops)
exec
utio
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e (s
ec)
H−WOP−KH−OSTP−K
S4: same S4: same
S4: sameS4: same
S5: faster
S5: faster
S5: fasterS5:faster
Figure 6.6: The execution time of K = 5
152 Finding K Optimal Social Trust Paths
Table 6.3: The comparison of execution time
AlgorithmsThe sum of execution time (sec)
4 hops 5 hops 6 hops 7 hops totalH-OSTP-K 1.4152e+003 4.1990e+003 9.4535e+003 2.1763e+004 3.6831e+004H-WOP-K 2.2380e+003 5.4336e+003 1.0445e+004 3.2421e+004 5.0538e+004difference 58.14% less 29.40% less 10.49% less 48.97% less 37.22% less
K) times from the priority queue, then in the following searching steps, H-OSTP-K
searches only K − J optimal social trust paths from vs to vt, and thus saves execution
time (see details in Optimization Strategy 2).
Through the above experiments conducted in sub-networks with different scales
and structures, we can see that H-OSTP-K is an effective and efficient algorithm for
MCOP-K selection in complex trust-oriented social networks.
6.5 Conclusion
In this Chapter, we have analysed the existing K optimal paths selection algorithms for
the top K shortest path selection problem. Then, in order to solve the NP-Complete
multiple QoT constrained K optimal social trust paths selection problem. we have
proposed an efficient heuristic algorithm H-OSTP-K based on the Dijkstra’s shortest
path algorithm and several novel search strategies. The results of experiments con-
ducted on real datasets of social networks demonstrate that H-OSTP-K significantly
outperforms the existing methods in the quality of identified social trust paths and the
efficiency.
The K optimal social trust path selection method proposed in this chapter can
identify more than one trustworthy trust paths, which helps deliver more reasonable
trust evaluation results.
Chapter 7
Trust Transitivity in Complex
Contextual Trust-Oriented Social
Networks
In social networks, if there is a social trust path linking two nonadjacent participants,
the source participant can evaluate the trustworthiness of the target one along an ex-
isting path based on the trust transitivity property (i.e., if A trusts B and B trusts C,
then A trusts C to some extent) under certain semantic constraints [63]. In each of
the selected social trust paths by the algorithms in Chapters 5 and 6, the computa-
tion of the value of trust for the target participant requires an understanding of how
trust is transitive along the trust path, which is a critical and challenging problem in
OSNs [48, 51]. In the literature, several trust transitivity models have been proposed
[48, 50, 51, 113, 124], but they have the following drawbacks.
Firstly, as illustrated in Social Psychology [3, 76, 102], the social relationships
between participants (e.g., the one between an employer and an employee), the so-
cial positions of participants (e.g., a supervisor as a referee in his postgraduate’s job
application) and the preference similarity between participants (e.g., whether both of
them like to play badminton) have significant influence on trust transitivity. However,
to the best of our knowledge, these impact factors are not fully considered by existing
trust transitivity models. Secondly, a source participant may have different criteria in
evaluating the trustworthiness of the target participant [91], impacting on trust transi-
153
154 Trust Transitivity in Complex Contextual Trust-Oriented Social Networks
tivity results. However, the specification of evaluation criteria is not supported by any
existing method. Finally, trust transitivity formalized in the existing models does not
follow the nature of trust decay illustrated in social psychology, namely, trust decays
slowly in a certain number of early hops (specified by a source participant) from a
source participant, and then decays fast until the trust value approaches the minimum
[44, 61].
In this Chapter, we first propose a novel concept, Quality of Trust Transitivity
(QoTT) to illustrate the ability of a social trust path to guarantee a certain level of
quality in trust transitivity. Then, based on the properties of trust illustrated in social
psychology, a new Multiple QoTT Constrained Trust Transitivity (MQCTT) model is
introduced. Experimental results demonstrate that the proposed trust transitivity model
follows both the principles in social psychology and the properties of trust, and thus it
computes more reasonable trust values than existing methods.
7.1 Trust Properties and the Quality of Trust Transi-
tivity
In this section, we first analyze trust properties and then propose a novel concept Qual-
ity of Trust Transitivity (QoTT).
7.1.1 The properties of Trust Transitivity
As illustrated in social psychology, trust has the following properties:
Property 1: Subjective. As illustrated in social psychology [54, 91], trust is a
subjective phenomenon that is defined by the psychological experiences of the indi-
vidual who bestows it, reflecting subjective attitudes that affect participants’ thinking
based on subjective evaluation criteria that can vary in different domains.
Property 2: Transitive. Trust can be transitive from one to another with a discount
[23]. In addition, trust transitivity needs certain constraints [23, 63]. Namely, if A
§7.1 Trust Properties and the Quality of Trust Transitivity 155
trusts B in the domain of teaching C++, and B trusts C in the domain of repairing a
car, then the trust cannot be transitive from A to C via B in the domain of teaching
C++. However, if A also trusts B in repairing a car (in the same domain that B trusts
C), then trust can be transitive from A to C in this domain.
Property 3: Decay. In trust transitivity, trust decays with the increase of transi-
tivity hops along a social trust path [23]. In addition, the general decay is non-linear
[61, 91] and can be divided into three phases. Phase 1: (Slow Decay Phase) In this
phase, trust decays slowly in transitivity along a social trust path from a source par-
ticipant within a certain number of hops (e.g., from 1 to 3 hops in Fig. 7.1). This is
because the source participant may consider the familiarity with the trustee to extend
no more than a certain number of transitivity hops. Phase 2: (Fast Decay Phase) With
the increase of transitivity hops, the trust decay speed increases in trust transitivity
until the trust value approaches the minimum (e.g., from 4 to 6 hops in Fig. 7.1). This
is because that in this phase, the trustee is becoming stranger to the source participant
than the case in Phase 1. Phase 3: (Slow Decay Phase) When the trust value between
the source participant and the trustee is approaching the minimum, the trust decay
speed changes from fast to slow (e.g., from the 6th hop in Fig. 7.1). This is because in
this phase, the trustee has become a stranger to the source participant.
Let λ1 denote the number of hops of trust transitivity in Phase 1 (e.g., λ1 = 3
in Fig. 7.1) and λ2 denote the number of the hops where trust approaches to zero
in Phase 3 (e.g., λ2 = 8 in Fig. 7.1). Their values can be specified by participants
based on their own trust evaluation criteria in a certain domain [61, 91]. Then even the
trust transitivity follows the general trust decay trend along a social trust path, based on
different λ1 and λ2 values specified by the source participants, they can obtain different
trust transitivity results of the target along the social trust path.
156 Trust Transitivity in Complex Contextual Trust-Oriented Social Networks
1 2 3 4 5 6 7 80
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
transitivity hops
trus
t val
ueSlow decay phase
Fast decay phase
Slow decay phase
Figure 7.1: General trust decay with the increase of transitivity hops
7.1.2 Quality of Trust Transitivity (QoTT)
In Service-Oriented Computing (SOC), QoS embodies a set of attributes to illustrate
the ability of services to guarantee a certain level of performance [40]. Similar to
the QoS, we propose a novel concept, Quality of Trust Transitivity, which in general
incorporates any attribute that impacts on trust transitivity.
Definition 4. Quality of Trust Transitivity (QoTT) is the ability of a social trust
path to guarantee a certain level of quality of trust transitivity, taking trust (T ), social
intimacy degree (SI), community impact factor (CIF ) and preference similarity (PS)
as attributes.
7.1.3 QoTT Constraints
Based on Property 1 of trust, in our model, a source participant can specify multiple
end-to-end QoTT constraints for QoTT attributes as the requirements of the Quality
of trust transitivity along a social trust path. Let QoTT µ′ denote the QoTT constraints
§7.2 Multiple QoTT Constrained Trust Transitivity Model 157
for the aggregated QoTT attribute µ′ (µ′ ∈ {T, SI, CIF, PS}) in a social trust path.
Then the aggregated trust value, social intimacy degree and community impact factor
value of a social trust path can be computed by using the corresponding aggregation
methods in Eqs (5.1) to (5.3) proposed in Chapter 5.1.2. In the following, we introduce
a method for the aggregation preference similarity value between participants in a trust
path.
As illustrated in social psychology [76], if two participants have the same prefer-
ence to an object, they have a high preference similarity which does not decay with
the increase of the number of transitivity hops. Thus, the aggregated PS value of path
p(a1,...an) in a certain domain can be calculated by Eq. (7.1).
PSp(a1,...,an) =
∑n−1k=2 PSak
n− 2(7.1)
Then based on our model, a reliable trust transitivity result can be computed along
a social trust path, if and only if each aggregated QoTT attribute value of the social
trust path satisfies the corresponding end-to-end QoTT constraint.
Since the QoTT constraints, λ1 and λ2 in trust transitivity are subjectively specified
by source participant in trust transitivity, these parameters are called subjective impact
parameters.
7.2 Multiple QoTT Constrained Trust Transitivity Model
In this section, we propose a novel Multiple QoTT Constrained Trust Transitivity
(MQCTT) model, where both subjective impact parameters and objective impact fac-
tors are considered.
7.2.1 The Process of MQCTT
In a social trust path p(a1,...,an), with the λ1 and λ2 specified by the source participant a1,
we take aj+1 (where there are j hops between a1 and aj+1 (j ≤ n−1)) as an example to
158 Trust Transitivity in Complex Contextual Trust-Oriented Social Networks
trust valueFigure 7.2: Trust transitivity model
introduce the calculation of the trust transitivity result Ta1,aj+1by our MQCTT model.
Step 1 (average trust decay speed): Based on Property 3 of trust, trust decays
to zero when the number of transitivity hops is greater than λ2 (λ2 > 1). As depicted
in Fig. 7.2, we draw a Base Line that starts from coordinate (1, Ta1,a2), which corre-
sponds to the first hop of trust transitivity with the initial trust value Ta1,a2 and ends
at (λ2 + 1, 0), where the number of trust transitivity hops is greater than λ2, leading
to the trust value of zero. This line and its slope can illustrate the average trust decay
speed along p(a1,...,an) in trust transitivity.
Step 2 (intersection angle θ): After identifying the average trust decay speed,
based on Property 3 of trust, if j ≤ λ1, the trust decay speed should be slower than the
average trust decay speed. Therefore, (j, Ta1,aj+1) should be above the Base Line (i.e.,
Situation 1 in Fig. 7.2). If λ1 < j ≤ λ2 (j, Ta1,aj+1) should be under the Base Line
(i.e., Situation 2 in Fig. 7.2). A Deviation Line that starts from (1, Ta1,a2) and ends
at (j, Ta1,aj+1) can be drawn, where an intersection angle θ is formed (i.e., θ1 < 0 in
Situation 1 or θ2 > 0 in Situation 2). Since the Ta1,aj+1is determined by θ, λ1 and λ2,
in the following steps, we will introduce how to compute the value of θ, and further
compute Ta1,aj+1along path p(a1,...,an).
Step 3 (the scope of θ): Before computing the value of θ, we first determine the
§7.2 Multiple QoTT Constrained Trust Transitivity Model 159
scope of θ. Since trust decays in transitivity with the hops via the social trust path
from a source participant [23], the minimal value of θ is equal to the interaction angle
from the Base Line to the horizontal axis (i.e., ϕ1 in Fig. 7.2), which can be calculated
by Eq. (7.2). In addition, based on Property 3 of trust, if and only if j > λ2, Ta1,aj+1
decays to zero. We draw a Decay Boundary Line that starts from (1, Ta1,a2) and ends
at (j, 0) j > λ1 to indicate the trust decay boundary. Then the maximal value of θ is
equal to the interaction angle from Decay Boundary Line to the horizontal axis (i.e.,
ϕ2 in Fig. 7.2) minus ϕ1, i.e., ϕ2 − ϕ1, where ϕ2 can be calculated by Eq. (7.3). Then
θ ∈ (ϕ1, ϕ2 − ϕ1)
ϕ1 = arctan(Ta1,a2
λ2
), λ2 > 1 and ϕ1 ∈ (0,π
2) (7.2)
ϕ2 = arctan(Ta1,a2
j − 1), 1 < j ≤ λ2 and ϕ2 ∈ (0,
π
2) (7.3)
Step 4 (logistic function): As illustrated in Property 3 of trust, the general trust de-
cay follows the curve plotted in Fig. 7.1. Therefore, the increase of θ is non-linear and
follows the curve depicted in Fig. 7.3. In mathematics, the logistic function is known
to be the most accurate one to model phenomenons possessing non-linear increases
with such a trend, and has been widely used in the real-world, e.g., modeling the non-
linear population growth in ecology, the non-linear growth of tumors in medicine and
the nonlinearity of clamp signals in neural networks [64]. Therefore, to compute an
accurate θ value and further obtain a more reasonable trust transitivity result, we use
the logistic function as in Eq. (7.4) to model the increase of θ. The function curve is
plotted in Fig. 7.3.
θ =
[ 2∗ϕ1
1+e(ξ−j) ]− ϕ1 for 1 < j ≤ λ1
[2∗(ϕ2−ϕ1)
1+e(ξ−j) ]− (ϕ2 − ϕ1) for λ1 < j ≤ λ2
(7.4)
where ξ is the argument controlling the function curve.
160 Trust Transitivity in Complex Contextual Trust-Oriented Social Networks
Step 5 (computing θ value): After modeling the increase of θ by using Eq. (7.4),
it is necessary to calculate the arguments of Eq. (7.4), and further compute θ value.
From Fig. 7.3, we can see that ξ is the argument controlling the number of transitivity
hops when θ = 0. Then based on Property 2 of trust, if 0 < j ≤ λ1, then ξ > λ1,
which ensures θ < 0 (i.e., Situation 1 in Fig. 7.2). Otherwise if λ1 < j ≤ λ2, then
ξ < λ1, which ensures θ > 0 (i.e., Situation 2 in Fig. 7.2). Then ξ can be calculated
by Eq. (7.5) and Eq. (7.6).
τ = SIp(a1,...,aj+1) + CIFp(a1,...,aj+1)
+ PSp(a1,...,aj+1) + Tp(a1,...,aj+1)
(7.5)
ξ =
λ1 + τ1−τ
for 1 < j ≤ λ1
λ1 − 1−ττ
for λ1 < j ≤ λ2
(7.6)
Note that Eq. (7.5) and Eq. (7.6) have the following characteristics:
Characteristic 1: if 1 < j ≤ λ1 and τ → 0, then ξ → λ+1 and thus θ → 0. In such
a situation, the Deviation Line tends to coincide with the Base Line. Namely, the trust
decay speed approaches the average trust decay speed when all QoTT attribute values
approach zero.
Characteristic 2: If 1 < j ≤ λ1 and τ → 1, then ξ →∞ and thus θ → ϕ. In this
situation, the Deviation Line tends to be parallel with the horizontal axis. Namely, the
trust decay speed approaches zero, when all the QoTT attribute values approach one.
Similarly, we can obtain the same characteristics above when λ1 < j ≤ λ2, fol-
lowing the principles in social psychology and the properties of trust.
Step 6 (computing Ta1,aj+1based on θ): After computing θ based on Eq. (7.4)
and the slope of Base Line (denoted as k1) based on Eq. (7.7) respectively,
k1 =Ta1,a2
λ2 + 1, (7.7)
§7.2 Multiple QoTT Constrained Trust Transitivity Model 161
2 3 4 5 6 7 8 9 10 11
−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
0.5
ϕ2 −ϕ1, (ϕ2 = 1)
inte
rsec
tion
angl
e θ
ϕ
−ϕ1, (ϕ1 = 0.5)
ξ=5
ξ=6
ξ=8
ξ=7
y=
y=
transitivity hops
Figure 7.3: Increase of intersection angle θ
the slope of Deviation Line (denoted as k2) can be calculated with Eq. (7.8).
tan(θ) = (k1 − k2
1 + k1k2
), θ ∈ (−ϕ1, ϕ2 − ϕ1) (7.8)
After obtaining k2, Ta1,aj+1can be calculated by Eq. (7.9).
Ta1,aj+1= Ta1,a2 + k2 · j, 1 < j ≤ λ2 and k2 < 0 (7.9)
Ta1,aj+1is computed based on both objective impact factors (i.e., T , SI , CIF and
PS), and subjective impact parameters (i.e., QoTT constraints, λ1 and λ2), thus it is
different from Tp(a1,...,aj+1)which is only one of the above factors impacting on Ta1,aj+1
value.
162 Trust Transitivity in Complex Contextual Trust-Oriented Social Networks
Table 7.1: Extracted sub-networksID Max hops Number of nodes Number of links1 4 61 1552 4 104 2373 5 158 3894 5 215 6195 6 228 6676 6 445 14187 7 551 32658 7 750 3301
Table 7.2: Selected trust transitivity modelsModel Number Category Strategy Authorsmodel 1 first multiplication Walter et. al [124]model 2 second average Golbeck et. al [48]model 3 third confidence-based Guha et. al [51]
7.3 Experiments on MQCTT
7.3.1 Experiment Settings
Firstly, in order to evaluate the performance of our proposed MQTTC model, we con-
duct experiments on sub-networks of different scales and structures, extracted from
the Enron email dataset1 which contains 87,474 nodes and 30,0511 links. This dataset
has been widely used in the studies of social networks [96, 117]. We randomly se-
lect 8 pairs of source and target participants, and then extract the corresponding 8
sub-networks between them by using an exhaustive search method. Among these sub-
networks, the maximal length of a social trust path varies from 4 to 7 hops, following
the small-world characteristic [50]2. These sub-networks are listed in Table 7.1.
Secondly, to compare MQCTT with existing trust transitivity models, we select one
model from each of the categories of the existing trust transitivity methods introduced
in the Chapter of Literature Review (Chapter 2) and list them in Table 7.2). In addition,
we select three domains in our experiments, including (1) product sales, (2) hiring
1http://www.cs.cmu.edu/enron/2The average path length between any two nodes is about 6.6 hops in a social network
§7.3 Experiments on MQCTT 163
Table 7.3: Subjective impact parameters of three domainsDomain (NO.) QoTT T QoTT SI QoTTCIF QoTT PS λ1 λ2
product sales (1) 0.1 0.05 0.05 0.05 3 4hiring employees (2) 0.05 0.05 0.1 0.05 4 5making friends (3) 0.05 0.05 0.05 0.1 5 6
employees and (3) making friends. The values of the subjective impact parameters
specified by a source participant are listed in Table 7.3. Furthermore, the values of
SI , CIF and PS can be mined in social networks by using data mining techniques.
But this is out of the scope of this thesis. Without loss of generality, the values QoTT
attributes are randomly generated by using rand() in Matlab.
Finally, as all trust transitivity models including MQCTT are used to compute the
trust value along a social trust path, we compare the most reliable trust transitivity
results of all models obtained from the optimal social trust path in a sub-network. The
optimal social trust path without QoTT constraints is selected by using the existing
optimal algorithm in [53], and the path with QoTT constraints in MQCTT is selected
by using the optimal algorithm in [83].
All four trust transitivity models are implemented using Matlab R2008a running
on an IBM ThinkPad SL500 laptop with an Intel Core 2 Duo T5870 2.00GHz CPU,
3GB RAM, Windows XP SP3 operating system and MySql 5.1.35 database.
7.3.2 Results and Analysis
7.3.2.1 Scenario 1: trust transitivity based on different subjective impact pa-
rameters
To investigate the performance of the MQCTT model with different subjective impact
parameters, we set the same T , SI , CIF and PS values in the three domains.
From the experimental results plotted in Fig. 7.4, we can see that each of the
existing trust transitivity models yields the same trust values in the three domains (e.g.
S1 in Fig. 7.4). However, based on Property 1 of trust, a source participant may have
164 Trust Transitivity in Complex Contextual Trust-Oriented Social Networks
02
46
8
1
2
30
0.2
0.4
0.6
0.8
1
sub−network IDdomain ID
T
model 1model 2model 3MQCTT
S1: same T value
S3: zero
S2: differentT values
Figure 7.4: Trust values computed based on different subjective impact parameters
different evaluation criteria in the trust transitivity of different domains, leading to
different trust values along the same social trust path. Thus, existing trust transitivity
models neglect this property.
In contrast, our MQCTT model considers different values of subjective impact
parameters specified by the source participant. Therefore, the trust values computed by
our MQCTT model are different in the three domains based on the source participant’s
different trust evaluation criteria (e.g., S2 in Fig. 7.4), following Property 1 of trust.
In addition, if no social trust path can satisfy the QoTT constraints in the sub-network,
or the number of transitivity hops is greater than λ2, the source participant will not
establish a trust relation with the target participant. Then the trust values of the target
participant are equal to zero (e.g., T = 0 in S3 in Fig. 7.4). This follows Properties 2
and 3 of trust. However, existing methods neglect these properties.
7.3.2.2 Scenario 2: trust transitivity with different social relationships
To investigate the performance of all models in trust transitivity with different social
relationships, SI value is decreased to SI ′ = SI/1.5, and the rest of the QoTT at-
§7.3 Experiments on MQCTT 165
02
46
8
1
2
30
0.02
0.04
0.06
0.08
0.1
0.12
sub−network IDdomain ID
TS
I−T
’ SI
model 1model 2model 3MQCTT
S5: TSI
−T’SI
=0
S4: TSI
−T’SI
>0
Figure 7.5: The results of TSI − T ′SI
tributes have the same values with those in scenario 1.
Fig. 7.5 plots the trust transitivity results computed based on SI (denoted as TSI)
minus those computed based on SI ′ (denoted as T ′SI), i.e., TSI − T ′
SI . We can see that
in some cases, TSI − T ′SI > 0 in the MQCTT model (e.g., S4 in Fig. 7.5). Namely,
the trust value computed by our MQCTT model decreases with the decrease of r value
when the social trust path satisfies QoTT constraints, which follows Principle 1. In
contrast, the trust values computed by each of the three existing trust transitivity mod-
els are the same, neglecting the influence of social relationships.
In addition, in MQCTT, if the aggregated SI and SI ′ values in a path do not satisfy
the corresponding QoTT constrains, TSI = T ′SI = 0 (e.g., S5 in Fig. 7.5). This follows
Property 3 of trust.
7.3.2.3 Scenario 3: trust transitivity with different social positions
To investigate the performance of these models in trust transitivity with different social
positions, CIF is decreased to CIF ′ = CIF/1.5. The rest of the QoTT attributes
166 Trust Transitivity in Complex Contextual Trust-Oriented Social Networks
02
46
8
1
2
30
0.02
0.04
0.06
0.08
0.1
sub−network IDdomain ID
TC
IF−
T’ C
IF
model 1model 2model 3MQCTT
S7: TCIF
−T’CIF
=0
S6: TCIF
−T’CIF
>0
Figure 7.6: The results of TCIF − T ′CIF
have the same values with those in scenario 1.
Fig. 7.6 plots the trust transitivity results computed based on CIF (termed as
TCIF ) minus those computed based on CIF ′ (termed as T ′CIF ), i.e., TCIF − T ′
CIF . We
can see that in some cases in domain 3, TCIF − T ′CIF > 0 in our MQCTT model (e.g.,
S6 in Fig. 7.6). Namely, the trust value decreases with the decrease of CIF value
when the social trust path satisfies the QoTT constraints, which follows Principle 1.
In contrast, the trust values computed by each of three existing trust transitivity models
are the same in each domain, neglecting the influence of social positions.
In addition, in MQCTT, if the aggregated CIF and CIF ′ value in a path do not
satisfy the corresponding QoTT constrains, TCIF = T ′CIF = 0 (e.g., S7 in Fig. 7.6).
This follows Property 3 of trust.
7.3.2.4 Scenario 4: trust transitivity based on different preference similarity
To investigate the performance of these models in trust transitivity with different pref-
erence similarity, PS is decreased to PS ′ = PS/1.5. The rest of the QoTT attributes
§7.3 Experiments on MQCTT 167
02
46
8
1
2
30
0.02
0.04
0.06
0.08
0.1
sub−network IDdomain ID
TP
S−
T’ P
S
model 1model 2model 3MQCTT
S9: TPS
−T’PS
>0
S8: TPS
−T’PS
>0
S10: TPS
−T’PS
=0
Figure 7.7: The results of TPS − T ′PS
have the same values with those in scenario 1.
Fig. 7.7 plots the trust transitivity results computed based on PS (termed as TPS)
minus those computed based on CIF ′ (termed as T ′PS), i.e., TPS − T ′
PS . We can see
that in some cases, TPS − T ′PS > 0 in our MQCTT model (e.g., S8 in Fig. 7.7).
Namely, the trust value computed by our proposed MQCTT model decreases with the
decrease of S value when the social trust path satisfies the QoTT constraints, which
follows Principle 1. In contrast, only the work in [51] follows this principle (e.g., S9
in Fig. 7.7), while other two models neglect the influence of the preference similarity
between participants.
In addition, in MQCTT, if the aggregated PS and PS ′ values in a path do not
satisfy the corresponding QoTT constrains, TPS = T ′PS = 0 (e.g., S10 in Fig. 7.7).
This follows Property 3 of trust. However, the existing methods, including the model
in [51] do not follow this trust property.
Summary: Based on the above experimental results and our analysis in the four
scenarios, we can see that our proposed MQCTT model not only follows the principles
in social psychology, but also follows the trust properties. Therefore, MQCTT can
168 Trust Transitivity in Complex Contextual Trust-Oriented Social Networks
compute a more reasonable trust value of the target participant than existing models.
7.4 Conclusion
In this chapter, we have proposed a general concept of Quality of Trust Transitivity
(QoTT) and proposed a novel Multiple QoTT Constrained Trust Transitive (MQCTT)
model in complex contextual trust-oriented social networks. Furthermore, we have
conducted experiments on the datasets of real social networks. Experimental results
have demonstrated that our MQCTT model follows principles in social psychology
and properties of trust, and thus it computes more accurate trust transitivity results
than existing methods.
The trust transitivity model proposed in this chapter can help compute reasonable
propagated trust values along the selected social trust paths, which can support a par-
ticipant to make a correct decision during the service selections or collaborations with
other unknown participants in OSNs.
Chapter 8
Conclusions and Future Work
8.1 Conclusions
In recent years, many people have joined in Online Social Networks (OSNs). In the
social networking platforms, the participants conduct a variety of activities, like seek-
ing employees and movie recommendations. In these activities, trust is one of the
most important indications for participants’ decision making. However in OSNs, most
participants do not have direct interactions previously (e.g., there is no previous in-
teraction between an employer and an employee, and there is no previous interaction
between a movie recommender and a movie recommendee). Therefore, evaluating
trust between two unknown participants becomes significant and necessary.
In this thesis, in order to provide an efficient and effective trust evaluation method
to deliver a reasonable trust value, three major contributions have been made. The
contributions are summarised below.
1. The first contribution of the work presented in this thesis is trust network extrac-
tion in contextual trust-oriented social networks. This is a fundamental step to
perform any trust evaluation methods.
(a) The current social network structures do not consider the social contextual
information, including social relationships, social positions, preferences
and residential locations. These social contextual information have signif-
icant influence on trust management. In our model, several social contex-
tual impact factors have been proposed. In addition, we have proposed a
169
170 Conclusions and Future Work
contextual trust-oriented social network structure which contains the above
factors, reflecting the social networks in real world scenarios better.
(b) In our trust network extraction method, a general concept Quality of Trust
Networks (QoTN) has been proposed, which contains the social contextual
impact factors, including the social intimacy degree, the community impact
factor, the preference similarity and the residential location distance as at-
tributes. The value of QoTN can illustrate the ability of the extracted trust
network to deliver a trustworthy trust evaluation result.
(c) As discussed before, a source participant may have different trust evalua-
tion criteria in trust evaluation, and social context can impact on the social
interactions between two participants. To address these issues, we have
proposed a social context-aware trust network extraction model with QoTN
constraints. In the literature, there are no algorithms for the NP-Complete
QoTN constrained trust network extraction problem. We have proposed
several approximation algorithms and heuristic algorithms. Experimental
results have demonstrated the superior performance of the proposed meth-
ods.
2. The second contribution of the work presented in this thesis is trust path selection
in contextual trust-oriented social networks. As evaluating trust via all the social
trust paths in a large-scale extracted trust network is computationally infeasible,
selecting those trust paths which can deliver most trustworthy trust evaluation
results is necessary and significant.
(a) In our trust path selection method, a general concept Quality of Trust (QoT)
has been proposed, which contains the social contextual impact factors,
including the social intimacy degree and the community impact factor, as
they have significant influence on trust path selection. The value of QoT
can illustrate the ability of a social trust path(s) to guarantee a certain level
of trust in trust evaluation.
§8.1 Conclusions 171
(b) In our model, a source participant can specify multiple end-to-end QoT
constraints to reflect their trust evaluation criteria. Then the trust path se-
lection problem is modeled as the classical Multiple Constrained Optimal
Path (MCOP) selection problem, which is NP-Complete.
(c) The proposed algorithms for trust path selection in the literature do not
consider the social context including social relationship and community
impact factor. We have proposed several approximation algorithms and
heuristic algorithms for optimal social trust path selection, and a heuris-
tic algorithm for K optimal social trust paths selection by considering the
social contexts and adopting our novel search strategies. Experimental re-
sults have demonstrated the proposed algorithms outperform the existing
methods in both the quality of the identified trust path(s) and the efficiency.
3. The third contribution of the work presented in this thesis is a novel model of
trust transitivity in contextual trust-oriented social networks. After identifying
the trustworthy social trust path(s), in order to compute the reasonable trust value
of the target, understanding how trust is propagated along the trust path is a
critical and challenging problem.
(a) In our trust path selection method, a general concept Quality of Trust Tran-
sitivity (QoTT) has been proposed, which contains the social contextual
impact factors, including social intimacy degree, community impact factor
and preference similarity, as they have significant influence on trust transi-
tivity. The value of QoTT can illustrate the ability of a social trust path to
guarantee a certain level of quality of trust transitivity.
(b) Then based on the properties of trust illustrated in social psychology, we
have proposed a new Multiple QoTT Constrained Trust Transitivity (MQCTT)
model. Experimental results demonstrate that the proposed trust transitiv-
ity model follows both the principles in social psychology and the proper-
172 Conclusions and Future Work
ties of trust, and thus it computes more reasonable trust values than existing
methods.
8.2 Future Work
In relation to foundational studies, trust situation between two participants is dynamic.
Therefore, in order to compute a more reasonable trust evaluation result, in addition to
the current proposed trust management models, we plan to study an efficient and effec-
tive method to compute the updated trust situation based on monitoring and analysing
the conversations between participants in OSNs in real-time. Then, based on the trust
information, a mining method will be proposed to find the most trustworthy participant
in a specific area, which can help individuals find high quality recommendations and
help companies find marketing targets in the area.
In relation to real applications, our work provides several key techniques to many
applications with social networks as the backbone. Based on them, a social network
based trust-oriented recommendation system can be developed, which maintains a so-
cial network with complex social contextual information. In such a system, our trust
management methods can help, for example, help a buyer to find the most trustworthy
seller who sells the product preferred by the buyer. Similarly, a new generation of so-
cial network based recruitment system and a new generation of social network based
CRM system can be developed, where the proposed trust management methods can
help an employer to find the most trustworthy potential employees, or help a retailer
to find loyal customers.
Chapter 9
Notations Used in This Thesis
Table 9.1: Notations Used in Chapter 3
FirstNotation Representation occurrenceCIFDi
A the Community Impact Factor of A in domain i Section 3.2.3deg−(A) the indegree of A Section 3.1.2.2deg+(A) the outdegree of A Section 3.1.2.3NE(v) the neighboring nodes of v Section 3.1PFDi
A A’s preference in domain i Section 3.1.1.2the preference similarity
PSDiA,B between A and B in domain i
Section 3.2.4
RL(A) the residential location where A lives in Section 3.1.1.3RLDA,B the residential location between A and B Section 3.2.5
SC the social context in a social network Definition 1SIAB the Social Intimacy Degree between A and B Section 3.2.2SPDi
A A’s social position in domain i Section 3.1.1.1SR
TYj
A,B the jth type of social relationship between A and B Section 3.1.2.1TDi
AB the trust value that A assigns to B in domain i Section 3.2.1
173
174 Notations Used in This Thesis
Table 9.2: Notations Used in Chapter 4
FirstNotation Representation occurrence
a set to store the expansionb− ClosedSet nodes in the Backward-Search Section 4.6.3
a set to store the candidates ofb−OpenSet expansion nodes in the Backward-Search Section 4.6.3
f − ClosedSet store the expansion nodes Section 4.6.3f −OpenSet store the candidates of expansion nodes Section 4.6.3
the number of the candidates of v−mgK ′in the search of a layer Section 4.6.2
the number of v−mgK ′′in the search of a layer Section 4.6.2
the number of the candidates of v+mgK∗
in the search of a layer Section 4.6.2
the number of v+mgK∗∗
in the search of a layer Section 4.6.2
the maximal outdegree of thed nodes in a social network Section 4.5.3
the number of the intermediateM nodes in a trust network Section 4.2.2
the complex trust-oriented socialMT (vs, vt) network between vs and vt
Section 4.5
the number of the correspondingN links in a trust network Section 4.2.2
OpenSet store the candidates of expansion nodes Section 4.5preceding neighboring nodes of vb
PreNE(vb) (the nodes have direct links to vb)Section 4.6.3
QoTN Quality of Trust Network Section 4.2.2the normal distribution based
SCP (vf → vt) selection probability between vf and vtSection 4.3.2
the context similarity based selectionSCPDi
vf ,vt probability between vf and vt in domain iSection 4.6.2
the social context similaritySmiDi
vf ,vt between vf and vt in domain iSection 4.6.2
U the utility of an extracted trust network Section 4.2.3the status indicates whether a
v.bvisit node is selected in Backward-Search Section 4.6.3
vexp an expansion node Section 4.3.2vf a feasible node Section 4.3.2
the status indicates whether av.fvisit node is selected in Forward-Search Section 4.6.3
175
Table 9.3: Notations Used in Chapter 4 (continued)
FirstNotation Representation occurrence
vm an intermediate node Section 4.2.1a marginal node which has a low
v+mg probability to connect with the target Section 4.6.1
a marginal node which has a lowv−mg probability to connect with the target Section 4.6.1
vs and vt the source and target respectively Section 4.2.2λh the threshold of search hops Section 4.3.2
Table 9.4: Notations Used in Chapter 5
FirstNotation Representation occurrence
the aggregated value of QoT attributeAQµ(p)
(µ ∈ {T, SI, CIF}) of path pSection 5.6.2
BLP backward local path Definition 4CBLP composite backward local path Definition 6
the aggregated community impact factorCIFp(a1,...,an) of path p(a1,...,an)
Section 5.1.2.3
FLP forward local path Definition 5fp
f(u)+b(δ)vs→vn→vt the foreseen path from vs to vt via vn Section 5.4.1
Fp(a1,...,an)the utility of path p(a1,...,an) Section 5.1.3the social trust path identified by
pbackwardvs→vt the Backward Search procedure Section 5.6.2
the BLP from vk to vt withp
b(CIF )vk→vt the maximal aggregated CIF value Section 5.6.2
the BLP from vk to vt withp
b(SI)vk→vt the maximal aggregated SI value Section 5.6.2
the BLP from vk to vt withp
b(T )vk→vt the maximal aggregated T value Section 5.6.2
the path from vn to vtp
b(δ)vn→vt with the minimal δ value Section 5.4.1
the CBLP from vk to vt withp
CBLP M (CIF )vk→vt part of p
b(CIF )vk→vt , M is the number of Section 5.6.2
the intermediate nodes of pb(CIF )vk→vt
176 Notations Used in This Thesis
Table 9.5: Notations Used in Chapter 5 (continued)
FirstNotation Representation occurrence
the CBLP from vk to vt withp
CBLP M (SI)vk→vt part of p
b(SI)vk→vt , M is the number of Section 5.6.2
the intermediate nodes of pb(SI)vk→vt
the CBLP from vk to vt withp
CBLP M (T )vk→vt part of p
b(T )vk→vt , M is the number of Section 5.6.2
the intermediate nodes of pb(T )vk→vt
the social trust path identified bypforward
vs→vt the Forward Search procedure Section 5.6.2
the path from vs to vnp
f(u)vs→vn with the maximal utility Section 5.4.1
QoT Quality of Trust Definition 3the end-to-end QoT constraint of QoT
Qµvs,vt attribute µ µ ∈ {T, SI, CIF}) Section 5.1.1
the aggregated social intimacy degreeSIp(a1,...,an) of path p(a1,...,an)
Section 5.1.2.2
the aggregated trust valueTp(a1,...,an) of path p(a1,...,an)
Section 5.1.2.1
vk an intermediate node in a sub-network Section 5.2.1vn an neighboring node of vs Section 5.4.1vu an unvisited node Section 5.2.3
gλ(p) the objective function defined in H MOCP Section 5.2.1ξ(p) the objective function defined in MCSP K Section 5.2.1δ(p) the objective function defined in H OSTP Section 5.4.1µ QoT attributes Section 5.1.1
Table 9.6: Notations Used in Chapter 6
FirstNotation Representation occurrence
fpFi+BKvs→vm→vt
K foreseen paths from vs to vt via vm Section 6.3.1K social trust paths from vt to vs
pBKvs→vt with the K minimal δ
Section 6.3.1
K social trust paths from vs to vtpFK
vs→vt with the K maximal utility Section 6.3.1
177
Table 9.7: Notations Used in Chapter 7
FirstNotation Representation occurrence
k1 the slope of Base Line Section 7.2k2 the slope of Deviation Line Section 7.2
the aggregated PS value of pathPSp(a1,...,an) p(a1,...an) in a certain domain Section 7.1.3
QoTT Quality of Trust Transitivity Section 7.1.2Ta1,aj+1
trust transitivity result between a1 and aj+1 Section 7.2.1λ1 the number of hops of trust transitivity in Phase 1 Section 7.1
the number of the hops where trustλ2 p(a1,...an) approaches to zero in Phase 3 Section 7.1
θ intersection angle Section 7.1µ′ QoTT attributes Section 7.1.3
178 Notations Used in This Thesis
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